A story came out today that the Jets have asked D'Brickashaw Ferguson to take a pay cut so the team can re-sign Fitzpatrick. I don't think publicly pressuring one of your most reliable players is the best way to negotiate, but that could just be me. Even if he does take a pay cut, that assumes Fitzpatrick will agree to whatever offer the Jets make.
Also, I don't think there is any leverage the team can use against Ferguson beyond "Help us out with this." I don't think there is a threat to release him if he doesn't take a pay cut. Even if the Jets do that, they're solving one problem while creating another - If Ferguson is gone, they can bring back Fitzpatrick, but then they'd have to bring in a new LT, cheap, and hope he plays well. Otherwise, Fitzpatrick will be welcomed back with the news that he'll be running for his life next season.