BOSTON – One hundred and thirty-seven players became free agents Monday according to Major League Baseball. If they don’t sign with their 2012 teams by 12:01 a.m. Saturday, they will be free to sign with any other team. 

The Red Sox have oodles of money to spend in the wake of the Great Dodger Bailout of August.  That’s a good thing, because they have massive holes to fill. 

It will be an interesting winter to watch how GM Ben Cherington rebuilds this team.  He will undoubtedly make some moves via trades, and will be involved in deals that might not grab headlines.

Yet there are some free agents who could help this team, players who are there for the taking if the price is right.

Here are a few big names on the market and how they could (or can’t) help the Red Sox. 

1. Two who should come back. David Ortiz and Cody Ross weren’t part of the problem in 2012, and they should be part of the solution in 2013.  Both understand what it takes to succeed in Boston, and both want to continue playing here.  Cherington may have to overpay (especially for Big Papi), but he needs to add to the current roster. Subtracting two bats from the lineup would make the rebuilding even more difficult.

 2. Avoid the biggest names. Josh Hamilton and Zack Greinke will get the most attention, but neither is a great fit for Boston.

We assume Red Sox management is going to avoid contracts of five or more years, and it’ll probably take at least that many for either of these players.  While the Sox need help in both the outfield and the rotation, these guys aren’t worth the commitment.

Nick Swisher is another big name the Sox would do well to pass on, although he will not be as sought after following his brutal postseason with the Yankees. 

3. Bring a little character into the clubhouse. We all know there have been chemistry issues in the Red Sox locker room the past two years.

Torii Hunter is a veteran who could add the type of leadership Manager John Farrell would love to have. He’s 37, and probably can be had for a two-year deal. He might be getting old, but he showed in 2012 that he can still hit (.313 average, 16 homers, 92 RBI.) 

4. More OF help? Michael Bourn would give the Sox a little speed (103 stolen bases in the last two seasons), and he’s an outstanding defensive outfielder. He might be a name to watch if Ross chooses to go elsewhere, or if the Sox want to bring in a left-handed hitter to platoon with the right-handed Ross. 

5. Who replaces Adrian Gonzalez. For years, Mike Napoli has been a certified Red Sox killer. He has a ridiculous career OPS of 1.075 against Boston and has 15 regular-season homers in 38 games against Sox pitching. If he’s willing to make the move to first base, he could help the team he’s feasted on. And he could add catching depth. 

6. Dealing a catcher? If the Red Sox choose to use Jarrod Saltalamacchia or Ryan Lavarnway in a trade, they might look for the next Kelly Shoppach to come in and add veteran depth.  Napoli could be part of that solution, or they could go the free-agent route with Russell Martin (21 homers, but just a .211 average with the Yankees) or A.J. Pierzynski. Pierzynski is still a productive player, but is not someone you bring in to help calm a contentious clubhouse. 

7. Rotational help. If the Red Sox bypass Greinke, there are other options out there. Anibal Sanchez began his career in the Red Sox system, Hiroki Kuroda showed what he can do on a one-year contract, Edwin Jackson has experience in the AL East, and Kyle Lohse will draw a lot of attention. Any of them would help a Sox rotation that was near the bottom of the game statistically last season.

8. A call to the pen. The bullpen has enough young arms to succeed in 2013, but a veteran like Mike Adams or Jonathan Broxton could help.

None of these players will make a splash like Carl Crawford did two years ago, but we now know that’s not really what this team needs. 

Cherington will be looking to find players willing to sign short-term deals. They are out there. And as of this weekend, they’ll be looking for work.

 Tom Caron is the studio host for Red Sox broadcasts on the New England Sports Network. His column appears in the Press Herald on Tuesdays.