If the team's assistants do not change, then Patterson will change head coaches, a source toldThe Austin American-Statesman.
"Steve Patterson thinks the status quo is unacceptable," another source told the Dallas Morning News.
Barnes and Patterson have had two face-to-face meetings, The Statesman reported Thursday, but the tenor of those meetings was not immediately clear.
Barnes has more wins than any other Texas basketball coach, and has led the team since 1998. He received a contract extension in the 2014 offseason, but his teams have struggled of late.
The Longhorns spent much of 2015 ranked in the Top 25, but finished with an 8-10 record in the Big 12. Texas lost 10 of its last 16 games, including a Round of 64 exit to Butler in the NCAA tournament.
Texas has not made it past the Sweet 16 since the 2008 NCAA tournament, and is 2-6 in the Big Dance since then.
Barnes' current contract runs through the 2018-19 season. His base salary was $2.55 million this season, according to The Statesman.
- Will Green