Stoops, fresh off the Sooners' stunning upset of Alabama in the Allstate Sugar Bowl, did little to quell rumors he may have the inside track to Cleveland's coaching vacancy.
While making the media rounds Friday, Stoops was asked about any connection to Cleveland, and the Youngstown, Ohio, native was coy with his responses.
"You never know," Stoops told Oklahoma writers.
Pressed on the issue and whether it was speculation, Stoops said, "There's a lot of that."
And is that all?
"Sure," he said.
This isn't the first time Stoops' name has popped up when Cleveland has been looking to hire a coach. His Ohio roots have made him a natural candidate, but the 53-year-old has chosen to stay in the college ranks, keeping the Sooners among the nation's elite programs.
Stoops has a 160-39 record at Oklahoma and became the only coach to win all four BCS bowls -- Sugar, Orange, Rose and Fiesta -- on Thursday night when the Sooners beat the third-ranked Crimson Tide 45-31.
Stoops received a contract extension in July through the 2020 season. He signed a seven-year, $34.5 million deal in 2011.
The Browns are in coaching search mode again after firing Rob Chudzinski last week after one season. Owner Jimmy Haslam and CEO Joe Banner vowed to get their second coaching search in just more than a year "right" this time, and landing Stoops would certainly win approval points from a skeptical Cleveland fan base tired of consistent losing.
The Browns have lost at least 10 games in each of the past six seasons and are looking for their seventh full-time coach since 1999.
On Dan Patrick's national radio show, Stoops was asked if he will ever coach in the NFL.
"That's something you never know will come your way," he said. "In life, things change from year to year and time to time, and right now I love what I'm doing and the people I work with at Oklahoma. So right now, it's not something I'm looking to pursue, but you never know down the road."
But earlier in the day, Stoops told ESPN Radio's Colin Cowherd that he hadn't heard of the rumors linking him to the Browns.
"I haven't heard that," Stoops told Cowherd. "But in the end, I don't ever acknowledge or deny one way or another whenever anyone has any interest in me. That's always a personal deal."
The Browns would not be averse to hiring a coach without NFL experience, especially one of Stoops' stature. Haslam went hard after Chip Kelly last year, but the former Oregon coach turned down Cleveland's offer before accepting Philadelphia's job. Kelly now has the Eagles in the playoffs, while the Browns are again looking for a coach.
Seattle defensive coordinator Dan Quinn met with the Browns earlier this week, and the team was scheduled to interview Arizona defensive coordinator Todd Bowles on Friday.
Haslam and Banner will reportedly interview New England offensive coordinator Josh McDaniels on Saturday. The 37-year-old McDaniels went 11-18 as Denver's head coach before he was fired in 2010, and is said to be ready for another shot as a head coach. The Browns can interview McDaniels because the Patriots have a playoff bye this weekend.
The Browns are also reportedly interested in speaking with Auburn Tigers coach Gus Malzahn, who is preparing his team for Monday's BCS title game against No. 1 Florida State.
The team is not commenting during its search.
The Associated Press contributed to this report.