Martin talked with Vols officials Monday, sources at Tennessee told ESPN.com, with the coach and athletic director Dave Hart meeting Monday night.
Martin had met Sunday with Marquette officials, and there was significant interest from the Golden Eagles in hiring him away from the Vols, multiple sources told ESPN.com.
Marquette is pursuing a replacement for Buzz Williams, who left after six seasons to take over as coach at Virginia Tech.
Martin's buyout with the Vols is set to decrease from $2.6 million to $1.3 million on April 1, according to a source.
Martin led Tennessee to a 24-13 record this season, 11-7 in the SEC. The Vols lost to Michigan in the Sweet 16 on Friday in Indianapolis after beating Iowa in the First Four in Dayton and then UMass and Mercer in the rounds of 64 and 32, respectively, in Raleigh last week.
Martin, who took the Vols to the NIT in his first two seasons in Knoxville after replacing Bruce Pearl, played at Purdue and was a head coach at Missouri State before landing at Tennessee.
Marquette interim athletic director Bill Cords is conducting the search for the Golden Eagles.
Former UCLA coach Ben Howland and current Duke assistant Steve Wojciechowski have also been considered for the job, sources have told ESPN.com.
ESPN.com's Andy Katz and Jeff Goodman contributed to this report.