Lynn previously interviewed for the 49ers' head-coaching vacancy earlier this month before the 49ers hired Chip Kelly. Lynn also interviewed for the Dolphins' head-coaching job before they hired Adam Gase.
Lynn, 47, played running back for the 49ers in 1995 and 1996. He has been a full-time NFL running backs coach since 2003 and has been a part of Rex Ryan's staff since 2009.
The Bills had the NFL's top-ranked running game this season in both rushing yards (2,432) and yards per rush (4.78).
Fox Sports reported Lynn's latest interview with the 49ers earlier Wednesday.