“It’s been pretty busy,’’ said an American League general manager. “There’s a more aggressive nature out there to get something done.’’

As the Red Sox close in on Adrian Gonzalez, there are still big-name free agents in play and big names that may be involved in trades.

Here’s a look at the hot players who could find new homes this week:

■Carl Crawford. Will anyone really go eight years and $150 million-$160 million? For sure.

The Yankees, who can pay Crawford a ton, are now in the hunt, though they haven’t yet held the recruiting meeting that so many major free agents tend to have with teams courting them. Crawford’s representatives have been saying to all interested parties that this negotiation may take a while because while there’s an obvious market, there’s also an emerging one. They want the Yankees and Rangers to get into it along with the Red Sox and Angels.

It’s hard to imagine that the Sox would make an eight-year commitment, given that they did everything they could to get out of the eight-year, $160 million Manny Ramirez contract, even though Ramirez was an extremely productive player.

Theo Epstein is not a fan of long-term deals; he views them as necessary evils at times. He dished out five years to John Lackey last winter but would go only so far with Jason Bay and Matt Holliday. The Sox were willing to go seven years with Mark Teixeira, who signed an eight-year deal with the Yankees.

At the end of an eight-year contract, Crawford would be 37 years old. Speed guys tend to slow down after 32. Crawford’s power is starting to emerge, but would he be an ideal No. 3 hitter? That’s the question teams like the Angels will ask themselves. He is an excellent defender, though his skills would be somewhat wasted for 81 games in left at Fenway.

Crawford is from Houston, and playing in Texas might be more appealing to him than Boston or New York or even Anaheim. There are other moving parts involved, too. The Yankees would have to trade Curtis Granderson or Nick Swisher before considering a deal for Crawford.

■Cliff Lee. It seems to be a two-horse race between the Yankees and Rangers. The half-dozen other teams who once showed interest are watching and waiting to see how it plays out. Lee has been visited twice by the Rangers and once by the Yankees during the courting process. It appears the Rangers will draw the line at five years for the 32-year-old lefthander, but the Yankees could put it over the top with a sixth year.

The question is, does Lee go to New York for the money or does he take a five-year deal in the $100 million range to keep his family in Texas, a mere hour flight from their Arkansas home?

If he wants to be with a winner, Texas now falls into that category. We will see whether the convenience of being close to home and in a less-hectic market are indeed meaningful to Lee.

■Jayson Werth. It sure looks as if the Tigers and Red Sox are the most interested and in the best position to offer a long-term contract. The reports are that Werth wants a six-year deal, but neither Detroit nor Boston appears inclined to commit for that long.

The Tigers, who already pulled off a reasonable four-year, $50 million deal for Victor Martinez, do have a good relationship with Scott Boras and have been able to consummate deals as a result of owner Mike Ilitch opening up the wallet.

If the Sox were to land Werth, it will be interesting to see where they play him. They have a very good right fielder in J.D. Drew who could move to left. And Werth can also play center.

■ Adrian Beltre. The Orioles need a big bat, either in the outfield or at a corner infield position, which is why they’re enamored with Beltre. He also is drawing interest from the A’s and Angels. Beltre told our Peter Abraham at David Ortiz’s charity golf tournament in the Dominican Republic that he preferred to stay with Boston. But with Gonzalez, the Sox may be out of the bidding.

“I was having a good day until you told me that,’’ Maddon quipped.

Maddon will be dealing with his first mass exodus of players this offseason. He’ll lose Carl Crawford and virtually his entire bullpen. But Maddon believes the Rays will be able to pick off a bargain player who can be plugged into the lineup and give the Rays at least a good fraction of what Crawford did.

“Carl is a big loss, that goes without saying,’’ said Maddon. “He will bring to whatever team he goes to a tremendous work ethic and is not affected by anything from one day to the next.

“He has a great sense of humor, very cunning. The players in our clubhouse will miss him, and he’ll be an asset to whatever clubhouse he joins. He’s obviously a great talent and he deserves everything he gets.’’

Maddon talks about Desmond Jennings, a 24-year-old Crawford clone (in terms of being a gap hitter and fast), perhaps being able to replace Crawford over time.

“He didn’t have the best of years, so he needs to come in and be very good and show us that he’s ready to be a consistent major league player,’’ he said.

Asked if he could be a younger Crawford, Maddon said, “The next couple of years will tell us that. He has the tools.’’

After hitting .325 in 32 games for Triple A Durham in 2009, Jennings dipped to .278 over 109 games last season.

The biggest challenge will be to replenish the bullpen. Maddon already lost Joaquin Benoit to the Tigers and expects to lose closer Rafael Soriano. There’s not much chance that Grant Balfour and Randy Choate stay aboard, either.

“We’re talking about losing the seventh, eighth, and ninth innings there,’’ Maddon said. “We have a chance to keep [Dan] Wheeler, but for us to get back to the 90-win category, we have to build a bullpen like we had last season, and that’s not going to be easy.’’

Maddon said the organization discussed placing surplus starting pitchers in the bullpen, but decided against it. There has been talk of dealing James Shields for more offense.

“There are a lot of relievers out there,’’ Maddon said. “We have to be able to get four or five and build a bullpen like we had last season. There’s some luck involved. We have to hope the relievers we get jell like the staff we had last season. There’s nothing that can hurt a team more than losing leads in the late innings.’’

To those who think the Rays may not be a contender?

“Don’t count us out yet,’’ Maddon said. “We still have a good rotation and a lineup with good athletes. We’ll probably pick up a hitter or two. It’s challenging, but our staff does such a great job.’’

It’s not hard to figure Pavano’s value, given recent signings. Ted Lilly got a three-year, $33 million with the Dodgers. Jorge De La Rosa signed a two-year, $21.5 million deal with the Rockies, with a third-year player option worth $11 million. Bronson Arroyo extended his contract with the Reds for two years at $23.5 million.

The only aberration was workhorse Jon Garland signing a one-year, $5 million deal (with incentives and an option) with the Dodgers. Even Dodgers righty Hiroki Kuroda signed a one-year, $12 million deal. Pavano would surely fall on the higher end of those figures.

Pavano has drawn interest from the Nationals, Brewers, Twins, and Marlins. The Nationals and Brewers have been very aggressive from the start.

Agent Tom O’Connell said he will not be affected by when and where Cliff Lee signs.

“We’ll do our own thing,’’ O’Connell said. “When we feel the time is right, we’ll sign a deal. We’ll have more meetings this week.’’

Asked whether he thought a deal would be done at the meetings, O’Connell said, “Hard to say right now.’’

Updates on nine 1. Adam Dunn, 1B/OF/DH, White Sox — The Red Sox considered Dunn as a first base possibility, but his defense was too subpar. Everyone loves Dunn’s power and ability to get on base, but his strikeouts and his defense are downers. He should be a force in the White Sox lineup, and if they can couple him with Paul Konerko, it could be a devastating left-right punch.

2. Johnny Damon, OF/DH, free agent — He still wants to have a Boston address next season, but it was learned that one reason Damon didn’t take the Red Sox’ bait to rejoin them at the trading deadline last year was that he had hurt his ankle and didn’t feel he could give them what they wanted. All indications are that Damon is fine now.

3. Manny Ramirez, DH/OF, free agent — Though he feels he needs to DH, he seemed a better fit for the Giants than Pat Burrell. Ramirez didn’t have a good year at the plate, but he can still hit. Defensively, he and Burrell are at least on a par. Ramirez may have options in Toronto, Baltimore, and Tampa Bay, but he’ll have to play on the cheap.

4. Zack Greinke, RHP, Royals — It’s becoming clearer that he will be moved this offseason. There is much debate over whether Greinke would go to New York, and a source who has known him for years thinks it’s highly unlikely. The same source said Boston would have a better chance. Texas (if it doesn’t re-sign Cliff Lee), Milwaukee, Baltimore, Washington, and Minnesota would seem to have a chance of obtaining the 2009 AL Cy Young winner.

5. Russell Martin, C, free agent — This is a classic change-of-scenery guy. He never lived up to his potential in Los Angeles, but at age 27, there’s still hope. The Yankees may be intrigued now that Jorge Posada has been told he’ll DH more than he catches, a Victor Martinez-type role. At the end, the Dodgers were toying with making Martin an infielder (second base) to take the pressure off so his offense would flourish. But when they couldn’t work out a contract, they decided to let him go and signed Juan Uribe to play second base.

6. Jonathan Papelbon, closer, Red Sox — Given that he’s at the end of his arbitration, it’s reasonable to think the Sox have shopped him and/or listened to offers this offseason. One team to watch is the Rangers, who have considered moving Rookie of the Year closer Neftali Feliz to the rotation. While the Rangers project Alexi Ogando in a closing role, it may be tough for a team that went to the World Series and has money to spend not to consider Papelbon.

7. Bobby Jenks, closer, free agent — Other than Martin, he’s probably the biggest non-tender out there. The White Sox gave up on him because he could never stay in shape. But one scout said, “If a team can get him to understand what he’s throwing away by not taking it seriously, you might have a pretty good bullpen arm for a couple of years.’’ He could be someone the Red Sox, Rays, and Yankees look into. Only a precious few teams would give him a chance to close until he reinvents himself.

8. Hideki Okajima, LHP, free agent — He had a bad season, but over his last 15 appearances, he seemed to right the ship. He had a 1.38 ERA over 13 innings, allowing nine hits and two earned runs. Okajima had back issues for much of the year, too. He seems to be a great fit for a National League team, and an NL scout said, “There are teams who saw him before September who probably don’t have great reports on him, but the ones who stuck with him and saw him in September pretty much saw the Okajima who had a pretty nice run in Boston.’’

9. Rafael Palmeiro, 1B, retired — He appears on the Hall of Fame ballot for the first time. He has all the numbers to make it, but he will not have a check mark on my ballot. Anyone who tested positive for performance-enhancing drugs after the testing program was in place — after numerous chances to get their act together — will not receive my vote.

Short hops From the Bill Chuck Files: “J.D. Drew’s fielding, as measured by UZR, which calculates how many runs a player saved or gave up, dropped from 10.9 in 2009 to 3.8 in 2010. Jayson Werth, also a right fielder, saw his 2009 number of 4.3 drop to minus-6.9 last season.’’ Also, “Since 2004, Jim Thome and Manny Ramirez have each hit 208 homers. Albert Pujols leads over that time frame with 294, followed by Adam Dunn with 282.’’ . . . Daniel Nava will be honored Jan. 25 at a banquet in San Jose, Calif., as the Santa Clara County major league rookie of the year. And Sox farmhand Chris Balcom-Miller was named the Santa Clara County minor league pitcher of the year . . . The guest list continues to grow for the 72d Boston Baseball Writers Dinner. Umpire Jim Joyce, whose candor and courage after Armando Galarraga’s near-perfect game was one of the baseball season’s most memorable stories, will be honored at the Jan. 20 dinner at the Westin Copley Place. Tickets are $150. Send a check payable to The Sports Museum, 100 Legends Way, Boston, MA, 02114. For credit card purchases, call Rusty Sullivan at 617-624-1237 . . . Happy birthday tomorrow to Kevin Cash (33) and Adam Hyzdu (39).

Nick Cafardo can be reached at cafardo@globe.com. Follow him on Twitter @nickcafardo. Material from interviews, wire services, other beat writers, and league and team sources was used in this report.