Brown, 62, is second in career victories at Texas with 158, trailing only legendary Darrell Royal (167).
After nine consecutive 10-win seasons under Brown at Texas from 2001 to 2009, the Longhorns have gone 5-7 in 2010, 8-5 in 2011, 9-4 in 2012 and 8-4 this season.
Texas was hurt by numerous injuries this year but still had a shot at winning the Big 12 title before a 30-10 loss at Baylor last Saturday. That fourth loss made Brown the first coach in Texas history with four losses in four consecutive seasons.
Texas AD Patterson said earlier this week: "We continue to discuss the future of Texas football. Mack Brown has not resigned. And, no decisions have been made."
The UT Board of Regents is scheduled to meet Thursday.
Meanwhile, San Francisco 49ers coach Jim Harbaugh would not answer questions Thursday about his name being mentioned as a possible replacement at Texas.
"Are you trying to be funny?" Harbaugh said. "I don't ever talk about any jobs other than the one I have."