Andersen would replace Bret Bielema, who left Wisconsin for the top job at Arkansas.
Andersen led Utah State to an 11-2 record this year, including a Western Athletic Conference championship and convincing 41-15 victory over Toledo in the Famous Idaho Potato Bowl. He is 27-24 in four years with the Aggies.
There was no immediate comment from the university; however the Journal said state law requires the Badgers to wait until two weeks have passed since the posting of the job, That means the earliest the announcement could be made is Thursday.
ESPN.com said Andersen interviewed with Wisconsin officials Monday.