The 2016 TE class is very weak with 4 of the best 5 prospects staying in school. However, there are a couple players in the Senior Bowl that could rise to a Day 2 status. The Patriots already have a monster TE in Rob Gronkowski and have been looking for a depth at the position. In 2015, they featured Michael Williams as the #2 TE that was mostly used to block and was rarely targeted. The Patriots had also signed Scott Chandler in the offseason to be the 2nd TE, but he wasn't effective and was decreasingly used as the season wore on. The Patriots certainly would like to find depth at the position although the offense without a healthy Gronk is nowhere near as prolific as it normally is.
Nick Vannett: The Ohio State program continues to send in TE prospects that are better than their production at the school. Since they are primarily a run-first team, the TE gets few opportunities to make plays, although Vannett can get the job done. He profiles as an inline TE due to his size and blocking abilities. He's not going to ever be a prolific receiver, although his upside could be as a Heath Miller outlet receiver that can be sneakily effective on 3rd downs if everyone else is covered. In Year 1, he would have to contribute on Special Teams and as the 3rd TE when the situation calls for one. He could wind up developing into the #2 TE for the Patriots a couple years down the road. Vannett is probably a late Day 2/early Day 3 pick in the draft.
Glenn Gronkowski: Part of the reason I included him is that he is Gronk's younger brother. Baby Gronk doesn't necessarily fit at either the TE or FB position, so he's going to have to prove to be an effective H-back matchup that dominates over linebackers. He measures in at 6'2" 238, which doesn't make him a candidate to play an inline role and he'd have to be moved around to generate matchups. I don't think he'll go before the third day of the draft due to the lack of a defined position and whatever team takes him is going to have to primarily use him on Special Teams in Year 1 with very little contribution on offense.
Jake McGee: McGee is more of a receiving TE than your traditional TE if the Patriots want to go that route. He started off playing at the University of Virginia before transferring to Florida. McGee could prove to be a sleeper in the draft since he has the size and athleticism to match up against linebackers and safeties in coverage. With a lot of coverage circling in on Gronk, the Patriots could theoretically bring McGee in to do some of the stuff Hernandez did in a Patriots uniform, although the former is nowhere near as prolific a route runner as the latter. If McGee runs under 4.7, they could bring back the element where they sent both TEs up the seam and throw to the one that's open.
The TE class on the surface isn't very good, but there are a few gems in the draft. It comes down to how teams would use these players. The Patriots have been looking for a 2nd reliable TE since Aaron Hernandez got arrested, then later convicted, for first degree murder. So far, they haven't found one yet.