According to a report by Memphis TV station WREG, Gruden was weighing an offer to coach the Volunteers that also would give him a piece of the Browns, who are owned by Jimmy Haslam -- brother of Tennessee Gov. Bill Haslam. Their father, Jim, played on the Vols' 1951 national championship team.
Gruden, a former NFL coach and current "Monday Night Football" analyst, said Wednesday on ESPN Radio's "Mike & Mike In The Morning" that there is "no truth" to the report. In past reports Gruden has been linked to various NFL and college openings.
"I'm just excited about 'Monday Night Football' and getting ready for the Giants and the Redskins," Gruden said. "I don't have time to get into all that stuff. I like what I'm doing, and I'm just trying to hang on to the job I have. Let's leave it at that."
Browns spokesman Neal Gulkis said Jimmy Haslam has no involvement in the University of Tennessee's coaching search, and the report that Gruden would potentially have an ownership stake in the Browns is "completely erroneous."
Tennessee didn't immediately return a call from The Associated Press. The Vols are looking to replace Derek Dooley, who was fired on Nov. 18.
Information from The Associated Press was used in this report.