It's not a good time to be looking to move a QB.
Only four or five teams are likely to enter the 2014 season with a starting QB who wasn't on their 2013 roster -- the Texans, Jaguars, Browns, and Vikings for sure, and perhaps the Raiders. Bridgewater, Bortles, and Manziel will likely fill three of those spots. The other one or two teams will have a bunch of options. Mallett might be one of the better options, but if the price is a 2nd rounder (or even a 3rd rounder), aren't those teams more likely to keep that pick to roll the dice on a projectable guy like Zach Mettenberger or Aaron Murray? (Feel free to substitute Taj Boyd, A.J. McCarron, or another QB who isn't likely to go in the 1st round for Mettenberger or Murray if you think I'm overrating those two.)
There's another four or five teams that should be in the market (the Jets, Dolphins, Titans, and Cards, and arguably the Rams) that will likely stick with the incumbent for another year. The Rams might grab a QB with the #2 pick, which could force a QB-starved team into the trade market, but otherwise I don't see any of these teams either trading for Mallett or making a move that would affect his market.
In sum, I think Mallett is worth more to the Pats as a backup QB than as a trade chip.