"I messed with Coach, [saying] he's getting too old to start up again somewhere else," McCarron said on ESPN's "College Football Daily" from Walt Disney World. "He told me he's not leaving. And I know Miss Terry [Saban's wife] well enough; she runs that house. And she's not allowing Coach to leave either. I think he'll be at the University of Alabama for a little while."
Speculation has been rampant after multiple media outlets reported that Texas coach Mack Brown may soon step down. Since Texas reportedly had reached out to Saban's representatives in the past, he became the top candidate to take over in Austin.
ESPN reported Wednesday that Alabama had readied an "offer of commitment" to make Saban the highest-paid coach in college football.
He signed an extension in March that pays him $5.62 million a year and runs through 2020.
Alabama athletic director Bill Battle would not address Saban's contract situation when contacted by ESPN on Wednesday.
"Coach Saban is spending his time recruiting and getting ready for a bowl game," Battle said from the Intercollegiate Athletics Forum in New York. "It's business as usual, and that's what we're getting ready for. We have a great recruiting class lined up. We have 14 prospects coming in this weekend, and [we're] looking forward to having them and looking forward to playing Oklahoma in the Sugar Bowl."
Battle was asked if he was concerned that Texas would target Saban.
"We're thinking about Oklahoma in our bowl game," Battle said, declining further comment.
Sources told ESPN.com's Chris Low that while Saban is recruiting he's not presently involved in the process of a contract extension -- adding that Saban is not worried about his deal.
The Associated Press contributed to this report.