Predicting trades is probably an exercise in futility, but I'll do it anyway. Trade back:
If Richardson is still on the board, I could see TB (19), SEA (20) and maybe BAL (22) interested in moving up.
If Richardson is gone and Hooker is still on the board, maybe WAS (16) wants to jump up 2 spots to get their guy? But maybe they stand pat and still get him.
If Bijan is on the board, DAL (26) and PHI (30) could give the Pats a call.
A guy like Levis or Carter could drop and someone wants to jump up and get them.
If they want to trade for future picks, that could open up a deal with a team in the early 2nd (like HOU, giving up #33, a 3rd/4th this year and a 2nd next year)
If the Pats want to trade up...ATL at 8 makes some sense as they only have 7 picks. And TEN doesn't have many picks sitting at #11.
I don't think they'd pay the price to move into the top 5. What would that take? 14, 46, next year's 1st and more? That's just not their style.