Texas regents are scheduled Thursday to consider a four-year contract extension to keep the 60-year-old Brown at Texas at least until 2020.
The move is seen as a response to rumors that surfaced after last season that Brown would retire soon or would be forced out.
Dodds declined to discuss specifics of the extension before Thursday's vote. Brown is paid $5.2 million a year with a $100,000 annual raise..
Texas went 8-5 last season with a Holiday Bowl win. Brown is 141-39 in 14 seasons at Texas and won the 2005 national championship.