Butler was scheduled to interview Michigan assistant LaVall Jordan on Thursday for their head coaching job, according to CBS Sports.
Athletic director Barry Collier said an offer could be made this weekend.
Butler is looking to replace Brad Stevens, who was hired by the Boston Celtics to be their new coach earlier in the week. The Bulldogs advanced to the NCAA championship game in 2010 and '11 under Stevens.
ESPN reported that Jordan is the frontrunner to lead Butler's program.
Butler assistant Brandon Miller is also being considered for the job. He interviewed for the job Wednesday, the Indianapolis Star reported.
Jordan, 34, played at Butler 1998-2001 and was a Bulldogs assistant under then-coach Todd Lickliter 2003-07. He has also worked as part of Iowa's coaching staff before spending the past three years with Michigan under John Beilein.