The Yankees realistically do not need Joe Mauer for the future of their catcher position to be safe. The Yankees have Jesus Montero, Austin Romine, Gary Sanchez, and J.R. Murphy, among others, as prospects at catcher. Also, they do have the amazing Francisco Cervelli!
The Red Sox, on the other hand, really do need Joe Mauer to be a free agent come 2011. They could re-sign Victor Martinez no problem, but with his defense declining, and the likelihood that he could ask for big bucks, the Red Sox would much rather spend the money on a younger, more defensively adequate option in Joe Mauer.
Honestly, if Joe Mauer does not re-sign with Twins, the Mets and the Red Sox seem like the two most obvious spots for him to land. The Yankees may be a fit, but why spend the money on someone they do not necessarily need THAT much. With Cliff Lee, Carl Crawford, and Jayson Werth hitting free agency, why not sign 1-2 of them instead?
Pujols is a bit of a different story. It is very, very likely that he re-signs with the Cardinals. I'd put it at 85%. If he does not sign with the Cardinals, the next best option is probably the Red Sox. The Red Sox do have prospect Lars Anderson at first base for the future, but he struggled a bit last season, if I remember correctly. Even if he did not struggle, they would much prefer Pujols.
The second best option if Pujols does not re-sign with the Cardinals? The Mets. Do you really think they will keep Daniel Murphy as their first baseman of the future if Pujols is available?
Overall, the Yankees should definitely want Pujols and Mauer to re-sign with their current teams. Lee, Crawford, Werth? Different stories. Thoughts?