He has a lot of leverage right now. The fact that there is only 1 year remaining on his deal gives him a great deal of leverage. As I said, he can "veto" any trade because nobody is going to trade for him without a new deal - and if they did, that puts him in an even better position where he gets to play AND be a free agent within 1 year (unless he was placed in the "horrible" position of being franchised for a measly $20+ million).
After this year, he has all the leverage he needs. The Patriots are not going to franchise him to keep him as a backup. And if they franchise him with the intent to trade him, no team is going to trade for him absent at least a deal in principle in place.
That's why, if he is smart, he will ride things out for 1 year until he is a free agent UNLESS some team he would be happy playing for makes him an offer he thinks is fair. He doesn't have to take whatever crap-ass offer he gets from some team the Patriots forced on him.