"I'd be OK with scheduling them in the right situation," Stricklin said Friday during a Chick-fil-A Peach Bowl event at Florida Field.
Florida and Central Florida last played in 2006, a 42-0 victory in the Swamp by the eventual national champion Gators. The teams had been scheduled to play again the following season, but UCF got out of the game and ended up paying a $100,000 buyout, according to documents released through a public-records request.
Stricklin said he and UCF athletic director Danny White have not spoken about scheduling a game.
"We haven't had a spot where we thought this made sense at this point," Stricklin said.
White, after seeing Stricklin's comments Friday, issued a statement saying he looked forward to trying to schedule a game with the Gators.
"I'm encouraged to hear that UF is open to the idea of playing us in football," White said in the statement, according to the Orlando Sentinel. "Since I've been here, it had been made clear to me there wasn't much hope of that. Our scheduling philosophy has been transparent since I arrived at UCF -- that we're open to a home-and-home series with any nonconference Power 6 opponent.
"Top-10 programs don't schedule 2-for-1 series where the balance is not in their favor. Our growing fan base and our student-athletes deserve better than that."
The American Athletic Conference, of which UCF is a member, has been pushing the "Power 6" brand all season. The current Power 5 is comprised of the SEC, ACC, Big Ten, Big 12 and Pac-12.
Many outsiders believed the 10th-ranked Gators (9-3) and No. 8 Knights (12-0) would meet in a bowl game this season, possibly in the Peach or PlayStation Fiesta Bowl. But Florida ended up facing Michigan in the Chick-fil-A Peach Bowl, and UCF will play LSU in the PlayStation Fiesta Bowl.
If the schools were to play in the future, Stricklin said it likely would need to be a 2-for-1 series. Florida agreed to play USF in a similar setup, with two games at Ben Hill Griffin Stadium (2022, 2025) and one at Tampa's Raymond James Stadium (2023).
White has made it clear he would prefer to schedule home-and-home series with Power 5 opponents because the school generates more revenue from a home game than it would from playing a payday game on the road.
"We do home-and-homes with like FSUs and Power 5 leagues," Stricklin said. "We haven't done any home-and-homes with non-Power 5 teams. I don't think we would start that.
"But I'd love to schedule [UCF] in a game."
Stricklin laughed off accusations that he worked behind the scenes -- he's a member of the College Football Playoff selection committee -- to prevent Florida from playing UCF in a New Year's Six bowl because the Gators had more to lose than gain in a potential in-state matchup.
"If you win the game, it counts one win," Stricklin said. "If you lose the game, it counts one loss. When I was at Mississippi State, they said don't play Southern Miss. We played Southern Miss. They had the same argument.
"To me, South Florida, you could say the same thing and we're not hiding."
Stricklin had to leave the room when the committee scheduled the Peach and Fiesta bowl matchups.
"People don't know. They give me a lot of credit," Stricklin said. "I have more power than I realize, according to them. People are going to say things when they don't know what they're talking about and that's what happening there."
The Associated Press contributed to this report.