If it's even money, he stays. He won't have to pay to move that way.
But anyone who has followed football over the past decade, and not just the team they root for, would know that he has always been a money-first guy. And to be honest, he has not done or said anything that should make people think that has changed. If he has said anything about taking less money to stay, or offering a hometown discount, provide the quote.
The only reason people think it's changed is because there is a segment of the population that is convinced everyone dreams of playing solely for the Patriots, and that they're the only team anyone would ever want to play for.
If anything, he is LESS likely to focus on winning a ring, since he now has one.