He's expected to make an announcement in the coming weeks.
Alvarez has been the Badgers' athletic director since 2004. The 74-year-old previously coached the school's football team from 1990 to 2005, winning the Big Ten three times and posting a 118-73-4 record. Additionally, he went 1-1 as an interim head coach across two separate bowl games during the 2012 and 2014 seasons.
The two-time Big Ten Coach of the Year, who also led Wisconsin to three Rose Bowl wins, was inducted to the College Football Hall of Fame as a coach in 2010.
Wisconsin has made a combined 49 appearances in bowl games (26) and NCAA men's basketball tournaments (23) since 1993-94, the most in the country, according to the Milwaukee Journal Sentinel's Jeff Potrykus.
Alvarez prefers deputy athletic director Chris McIntosh to replace him, sources told Potrykus.