Memphis television station WREG reported Gruden was weighing a Tennessee offer that would give him a piece of the Browns, who are owned by Jimmy Haslam - brother of Tennessee Gov. Bill Haslam. Their father, Jim Haslam, played on Tennessee's 1951 national championship team and has donated millions of dollars to the university.
Gruden, a former NFL coach and current ESPN analyst, said Wednesday on ESPN's "Mike & Mike In The Morning" show that there is "no truth" to the report.
"I like what I'm doing," said Gruden, who was a graduate assistant with the Volunteers and whose wife Cindy is a former Tennessee cheerleader. "I'm just trying to hang on to the job I have, to be honest with you."
Browns spokesman Neal Gulkis said the report was inaccurate.
"Jimmy Haslam has no involvement in the University of Tennessee head coaching search, and the report that Jon Gruden would potentially have an ownership stake in the Browns is completely erroneous," Gulkis said.
Tennessee is seeking to replace Derek Dooley, who was fired Nov. 18 after going 15-21 in three seasons.
Volunteers athletic department spokesman Jimmy Stanton said the university would not discuss details of its coaching search.
"We won't talk about any of the dynamics of the search until it is finalized," Stanton said.
Gruden, 49, helped the Tampa Bay Buccaneers win the Super Bowl in the 2002 season. He posted a combined 100-85 record and won five division titles in 11 years as an NFL head coach with the Oakland Raiders (1998-2001) and Tampa Bay (2002-08).
Gruden began his coaching career as a graduate assistant on Johnny Majors' Tennessee staff in 1986-87, but he hasn't worked in the college ranks since a one-year stint as Pittsburgh's wide receivers coach in 1991. His other college experience includes one year as Southeast Missouri State's passing game coordinator (1988) and one season as the University of Pacific's wide receivers coach (1989).