Tom Herman, offensive coordinator at Ohio State, is expected to be named head coach at Houston, according Bruce Feldman of Fox Sports.
Feldman attributed his information to a source.
Herman, 39, had been rumored as a possible candidate for the Michigan job.
Tony Levine was fired by the Cougars after four seasons; they were 7-5 in 2014.
Herman's Buckeyes led the Big Ten in scoring offense (45.2 points) and total offense (507.6 yards) this season, despite rolling through three quarterbacks due to injury – Braxton Miller, JT Barrett and Cardale Jones.
Barrett led the Big Ten in total offense with 314.3 yards per game.