I live in Minnesota right now and Mauer is the franchise for the Twins. He loves being in Minnesota so chances are, I doubt he would allow a trade (he has a no-trade clause I believe).
Additionally, he makes a lot of money. I'm going to sound like a broken record from my previous post in the Josh Hamilton thread but he doesn't fit the new direction the Sox want to take in regard to players who make too much money.
Joe Mauer won't be a catcher for much longer and the fact is, the Twins paid him the money he makes because he's amazing at catcher. Put him at first base or the OF he doesn't stack up well to his contemporaries who are paid at a similar level. He'd essentially be a guy whose paid 20 + million are year to hit at best 12 - 13 home runs with an amazing average. For him to make that much, he should be hitting closer to 30 + home runs a year.
Also, yet again, he's from Minnesota - and there's a big difference between Minnesota and New England. I know this first hand as I have spent 16 years in Boston and now 6 in Minnesota.