He probably will, but he seems like a player that the Twins may make an exception for, especially with Pohlad no longer in office (RIP). I'm not saying that the Twins will be able to beat out the Yankees in terms of spending, but with the help of Pohlad the Twins certainly have the resources available to make themselves known.
I know this is just speculation, but Mauer also doesn't seem to be as money-hungry as other players. I mean he has to know that he's a one of a kind player, but he doesn't seem as likely to screw his own team over for money. Obviously that's just speculation, as there are no facts to prove/disprove it, but I just don't see Mauer being a Yankee for the rest of his career.