Auburn athletic director Jay Jacobs subsequently confirmed the news.
"After careful evaluation of the last four years, I feel this is best for the program," Jacobs said via a prepared statement. "I believe we should compete for championships in men's basketball. It's time for somebody else to have a turn. We need to find somebody to come in here and take what we have here now and put some more in and compete for SEC titles."
Barbee never won more than six SEC games in any of his four seasons at Auburn.
The Tigers finished 14-16 overall, 6-12 in the SEC this season.