Multiple reports earlier Wednesday had Memphis targeting Smith. Sources told ESPN that the process has advanced to the point where Smith is the Tigers' No. 1 candidate.
Memphis is looking to replace Josh Pastner, who left to be the head coach at Georgia Tech last week. If Smith took the Memphis job, then the American Athletic Conference would have added a former national championship-winning coach in Smith, a former NBA Coach of the Year in Mike Dunleavy (hired at Tulane) and former Stanford coach Johnny Dawkins (now at Central Florida) in the past few weeks.
Smith, 64, received the John R. Wooden Legends of Coaching award on Friday in Los Angeles. He is one of two coaches to lead five schools to the NCAA tournament.
He coached at Kentucky from 1997 to 2007, leading the Wildcats to one national title in 1998 and 10 straight NCAA appearances. He coached Minnesota to the NCAA tournament in 2013 before being abruptly fired.
He led Texas Tech to the NCAA tournament last month in only his third season in Lubbock.
Smith previously coached at Georgia for two seasons and Tulsa for four.
Memphis is considered a top-25 job among college basketball coaches/administrators for its proximity to talent, its facilities and its storied history.