Lynch has privately expressed interest in playing for the Patriots should a move to his hometown Raiders fall through, the Boston Herald's Jeff Howe reported Monday.
Lynch visited the Raiders' facility last week as he considers making a comeback. The visit was cleared by the Seattle Seahawks, who own Lynch's rights.
Lynch, who turns 31 on April 22, retired from the NFL and Seahawks after the 2015 season. He has been on the reserve/retired list since May 2016.
Under terms of his existing contract, Lynch would be in line for a $9 million salary and cap hit in 2017, and he would be due a base salary of $7 million in 2018. He could potentially earn an additional $3 million roster bonus, according to ESPN.
Seahawks coach Pete Carroll said last week he recently talked to Lynch and confirmed the running back was considering a return to the NFL.
Carroll admitted he is not sure whether the Lynch could still be effective.
"I don't know," Carroll said. "It depends on how he's approached this offseason. He looked OK. The mentality that it takes to play this game the way he plays this game, he has to really be invested and ready because he goes deep when he plays. Whether or not that's still in him, the burn is still there, I couldn't tell that from talking to him. I know that he was playing with the idea."
Former Minnesota Vikings running back Adrian Peterson visited with the Patriots last week without striking a deal. The Patriots' lead back last season, LeGarrette Blount, remains unsigned after he scored a franchise-record 18 rushing touchdowns last season.
Lynch finished his nine-year NFL career with 9,112 rushing yards and 74 touchdowns in 127 games, and another 1,979 receiving yards and nine TDs.