When a player you signed a year ago for $10,500,000 is traded for a 6th round pick because he can't get along with his team mates, he's kicked off.
If he goes to NE, maybe he'll punch Brady in the eye the night before the Jets game. Being with the Pats isn't going to prevent him from getting injured.
There are only a few ways to deal with Harvin. You either just pay him, and put up with him. And watch him get his 600 or so yards before he gets injured or causes a problem in the locker room. Or you release him, then offer him the same contract he has now, accept for one small detail. The pay out is 5-6 million. Not 10-11.
I really doubt with his past behavior, and injury history there are many teams out there willing to to give him a 50 million contract, with guarantees.