Would not be surprised AT ALL. That doesn't mean I think it will happen though.
I can honestly say that I can't blame him for wanting to see what he can get in the free agent market. I would (if I wasn't born a fan of the team).
He's brittle and can't make it through a season. We already have one such QB lodged on IR.
Maybe at the beginning of his career it would have been worth it, but he has had some serious issues in the last few years.
FWIW, I just got off the phone with a ST rep. He said he's under the impression that they aren't even ready to get the notifications out, and last he knew they were waiting on a possible price increase across the board.