A television station in Mobile, Ala., reported, citing unidentified sources, that Muschamp would be named Auburn's coach Friday.
Muschamp agreed to become coach-in-waiting behind Brown, who has no plans to retire soon, last month. The deal more than doubled Muschamp's salary to $900,000.
Muschamp was the defensive coordinator at Auburn in 2007. Tommy Tuberville stepped down last week after 10 seasons as Auburn coach.