Ian Rapoport of NFL Network reported Lynch will meet with the Bills on Tuesday.
Lynch, 24, was a 2016 first-round pick for the Broncos but failed to pan out. He threw for 792 yards and four touchdowns against as many interceptions in five NFL games.
"I'm sad to see him leave, but I'm happy for him because he needs the change of scenery. I remember that second preseason game, we were playing against the Bears. He goes in and the crowd is just booing him. It does something to you as a player," Broncos wide receive Emmanuel Sanders told reporters.
The Bills traded AJ McCarron to the Oakland Raiders for a fifth-round pick earlier this preseason. Nathan Peterman, whose most notable NFL experience is a disastrous start as a rookie last season, has been named Buffalo's starter for Week 1.
The team is choosing to bring along first-round pick Josh Allen slowly. Allen was always viewed as a long-term project rather than an instant starter, but his losing the job to Peterman in camp is still a surprise.
That the Bills are looking for a veteran quarterback would suggest they're not satisfied with their current depth chart.
Lynch would likely compete with Allen for the backup spot.