His contract is going to make a trade more difficult. The fact that teams know the Jests will cut him if they have to will also hurt any trade value. Considering those factors means he likely wont get the Jests as much as what they would get for him otherwise.
Im guessing some team will come off of some kind of compensation to prevent buttfumble from hitting the market and being able to sign with one of the other 2 or 3 teams who may be interested. But, these teams may also think it might be worth letting him hit the market because then they could sign him at a much cheaper price than what his current contract will pay him next season.
Its difficult to say for those reasons. I know there wont be more than 3 or 4 teams with interest. Im sure there are teams desperate for a QB though who feels like they might be able to turn things around for him. The fact that there simply arent many options in the draft this year helps buttfumble out.
Maybe a 4th rounder. Maybe. Perhaps a 3rd, but thats probably the max. If a team with a stadium and/or practice facility with a lot of trees around making for extra leaf blowing duties during the season is interested, they may be willing to part with a pick for him.