Brohm, the former Louisville quarterback who just finished his first season as head coach at Purdue, has had discussions with Tennessee officials, sources told ESPN.
The Vols are trying to put an end to a whirlwind coaching search to replace Butch Jones, who was fired Nov. 12. The search seemingly ended with Ohio State defensive coordinator Greg Schiano on Sunday, but that deal was nixed after fans and state politicians expressed their outrage.
Tennessee also courted Mike Gundy, who announced Tuesday night that he was staying at Oklahoma State, where he has been head coach for the past 13 seasons. The Vols were prepared to make Gundy one of the highest-paid coaches in the SEC, sources said Tuesday.
Duke's David Cutcliffe has also turned down Tennessee, sources told ESPN.
Brohm, 46, guided the Boilermakers to a 6-6 mark this season. Prior to this season, Brohm coached at Western Kentucky for three seasons, compiling a 30-10 mark with the Hilltoppers.
As a player, Brohm spent time with six NFL teams over seven seasons, seeing action in just eight games. He also played one season in the XFL before making the transition into coaching.
If he were to leave the Boilermakers before Dec. 5, Brohm would owe $5 million to the university. The buyout would drop to $4 million if he leaves after Dec. 5.
ESPN's Adam Rittenberg contributed to this report.