Brown addressed the issue at Tuesday's Holiday Bowl press conference.
"[Athletic Director] DeLoss [Dodds] visited with me a couple days ago," Brown said. "I thought how grateful Sally and I are to Texas – the administration, DeLoss, [University President] Bill [Powers], the board of regents and our fans because they've been so great to us for 14 years.
"Unlike so many places in the country, we've never had a rift. Everybody is so honest and upfront with each other. I'm excited they're considering extending that. I want to be here for a long time.
"I think last year was a time in my life where I had to make some hard decisions about myself and about our program. We did start over and I've never been more excited about where we're going."
Dodds told the Austin American-Statesman that he hopes an extension will stop the rumors regarding Brown retiring or being forced out after this year.
Brown is one of the highest paid coaches in the country and is 140-39 in his 14 years at Texas. However, he's 12-12 over the last two seasons.
Asked if he sees himself as a Bobby Bowden type, coaching into his 80s, Brown said he doesn't know.
"Right now I'm just having fun," the Texas coach said. "I don't think anybody ever thinks about being coach [Joe] Paterno or coach Bowden because those just don't happen much, but I'm sitting here at 60 and I feel really healthy and I feel great and I love this staff and I love this team."
Brown said he never really thought much about what age he'd like to end his career until he named former Longhorns' defensive coordinator and current Florida head coach Will Muschamp "Coach in Waiting" back in 2008.
"That's the first time I ever even thought about what's fair—what's fair to Texas, what's fair to Will…we never had a date," Brown said. "I thought Will being 38, if he wanted to stay a long time, he could be a lifetime defensive coordinator at Texas and then take the head job, but none of us thought it would be two years, three years and Will was so hot, it didn't last long.
"Last year because we didn't play well and I didn't think I did a good job, it was the first time I had to sit down and really say, ‘What are we doing here? This isn't what we want for Texas.' Sally and I decided to go back and give it our best shot for as long as we could do it."
Brown has said all year that he's never felt so "re-energized" in his life. One reason he thinks coaching this year is somewhat easier than it was last year is due in part to team camaraderie and the fact that they simply just play hard. Last year the guys didn't.
"[The players] went back to it being about Texas and getting better," Brown said. "Seniors really reached out to the young ones whereas last year, we had some older guys who resented young ones playing and we had some griping. This year we have very minimal griping, very few problems, our academics are in the best shape they've ever been in, the attitude is great and Benny [Wylie] has been working them."
Texas has one of the nation's top recruiting classes coming in next fall and Brown is excited to see what guys like Johnathan Gray and Cayleb Jones can do when paired with Malcolm Brown, Joe Bergeron and Jaxon Shipley, for example. He wants to be here to see what the Longhorns can do down this next stretch, however long it may be.
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