According to Bleacher Report's Matt Miller, former Oregon tight end Colt Lyerla is "off the Patriots [Draft] board, as well as (at least) five other teams." Miller is extremely connected in the draft community.
Lyerla was a high school running back and linebacker with unparalleled athleticism. When he joined the Oregon Ducks and their high flying offense, he transitioned to tight end and was essentially Aaron Hernandez in their offense; he won with his athleticism and no one could keep up.
He's gone through a series of serious off-season incidents this past year, ranging from a cocaine arrest to dropping off the football team early in the season to four driving tickets in the past two years.
If that wasn't enough to get the Patriots to remove him from consideration, he called the tragedy at Newtown a "conspiracy". Any connection of interest between the Patriots and Lyerla is certain to alienate a large portion of the Patriots fanbase and isn't worth the team's effort to reconcile the situation.
If the Patriots want an alternative to Lyerla, there's the first round prospect Eric Ebron, as well as another troubling late round option in A.C. Leonard. Alternatively, free agent Dustin Keller is coming off of a huge knee surgery, but was more athletic than Lyerla coming into the league.