With only 35 days to go before pitchers and catchers report to Spring Training (Thank God), the free agent pool is starting to become more shallow. Brian Cashman told the media last week that he will not surrender a first round pick to sign one of the three remaining Type A free agents. With that in mind, let’s take a look at the Top 10 remaining free agents and gauge any potential Yankee interest.

1. Rafael Soriano, RP, Rays: I’ve written a lot on the former Ray closer, so you can check all of that out here. Soriano makes a lot of sense for the Yankees, but price is always a concern. Brian Cashman echoed that statement last week when he said he would not give up a first-round draft pick to sign Soriano. While it’s always possible that Cashman may go back on his word if the price is right, don’t expect to see Soriano in the Bronx in 2011.

2. Carl Pavano, SP, Twins: We know for sure that Pavano is not coming back to the Bronx. Pavano is close to closing in on a deal with the Twins.

3. Jim Thome, DH, Twins: The powerful lefty is only eleven homers shy of 600 for his career. Last season, Thome clubbed 25 dingers for the Minnesota Twins. With Jorge Posada already occupying the DH slot for the Yanks, another team will be able to promise 40-year-old lefty more at-bats and cash.

Update: The Rangers and Thome are apparently engaging in talks.

4. Vladimir Guerrero, DH, Rangers: At age 35, Guerrero had one of his best seasons in 2010. After smacking 29 home runs and driving in 115 runs, the future Hall of Famer does not have a job for 2011. After the Rangers signed Adrian Beltre, Guerrero’s path back to the Rangers was seemingly blocked. A reunion with the Angels is possible, but don’t expect to see him in the Bronx in 2011.

5. Andy Pettitte, SP, Yankees: It’s either Yankees or retire for the crafty lefty.

6. Manny Ramirez, OF/DH, White Sox: The goofy Ramirez is still looking for a job in 2011. Some team will give this big goof ball a one-year deal. Don’t expect it to be the Yankees or Red Sox, though.

7. Brian Fuentes, RP, Twins: One of A-Rod’s best friends after the 2009 post-season. The lefty reliever is seeking out $5 million/season and an opportunity to close. The Pirates have expressed interest as well as the Rays. The Yankees already have Mariano Rivera in the fold as well as lefties Pedro Feliciano and Boone Logan. Pass on the erratic Fuentes.

8. Kevin Millwood, SP, Orioles: The 36-year-old Millwood just finished the final season of a 5-year/$60 million contract. However, Millwood arguably had his worst season ever in 2010. In 31 starts, Millwood went 4-16 with a 5.01 ERA for the Orioles. The Yankees are seeking out an innings eater, which Millwood is, but Millwood’s inflated ERA pitching in the AL East makes me nervous. Pass on Millwood and let the Rockies or the Royals take a chance.

9. Grant Balfour, RP, Rays: Another player who would cost a first-round draft pick.  Balfour was good last season (2.28 ERA, 56 Ks in 55 innings), yet the cost associated with signing him is too great. Let another team sacrifice a first-rounder for him.

10. Johnny Damon, OF/DH, Tigers: Scott Boras said last week that he is not ruling out a potential Yankee/Damon reunion. However, that ship has definitely sailed. After averaging 19 home runs per season with the Bombers, Damon only clubbed eight last year for the Tigers. I won’t go into Damon’s defensive struggles, but the Yankees need a right-handed power bat that can play good defense. Not a lefty-bat with a noodle arm. Pass on Damon.