Numerous media outlets reported that Andersen interviewed in Madison on Tuesday. The local newspaper subsequently cited an anonymous source as saying Andersen was prepared to tell the Utah State staff about his departure.
Andersen, 48, led the Aggies to a 26-24 record over four seasons. Utah State played in each of the past two Famous Idaho Potato Bowls, losing 24-23 to Ohio in 2011, then beating Toledo 41-15 on Saturday.
Utah State won the Western Athletic Conference title this year, going 6-0 in league play and 11-2 overall. The Aggies were ranked No. 22 in the most recent BCS standings.
Andersen previously served as Utah's defensive coordinator for four seasons, and he was the head coach at Southern Utah in 2003, guiding the team to a 4-7 season. He played as a center for Utah in the mid-1980s.
At Wisconsin, Andersen would take over for Bret Bielema, who left Dec. 4 after seven seasons with the Badgers to become the head coach at Arkansas.
Athletic director Barry Alvarez, Wisconsin's former head football coach, will lead the Badgers (8-5) in the Rose Bowl against sixth-ranked Stanford (11-2).