Farmer was interviewed by the Dolphins nearly two weeks ago and turned down their invitation for a second interview. The team is expected to interview finalists soon, with Titans vice president of player personnel Lake Dawson and Dolphins assistant general manager Brian Gaine considered front-runners.
The Dolphins are searching to replace Jeff Ireland, whose six-year stint as GM ended Jan. 7 when he and owner Stephen Ross agreed to part ways. Miami faded late in the season to finish 8-8 and hasn't been above .500 since 2008, the longest such stretch in franchise history.
The Dolphins currently have Gaine running their personnel department at the Senior Bowl while the team searches for a general manager.
The Associated Press and ESPN.com Dolphins reporter James Walker contributed to this report.