Cristobal, a Miami native and a former Hurricanes offensive lineman and assistant, also has a lucrative contract offer from Oregon to remain Ducks coach.
Miami has not fired coach Manny Diaz, who continues to recruit for the school along with his assistants. Oregon assistants are also out recruiting Sunday and have not been informed about Cristobal's decision, sources said.
Cristobal on Sunday appeared on a videoconference call with Oklahoma interim coach Bob Stoops to announce the teams' matchup in the Valero Alamo Bowl. Neither coach took questions from the media. Cristobal, wearing an Oregon shirt, said his team looks forward to playing in the game. The call ended with Stoops wishing Cristobal luck on the recruiting trail.
Miami is set to make major investments in its program and wants to build around Cristobal and a new athletic director. The school is targeting Clemson athletic director Dan Radakovich with a multimillion-dollar contract, but other candidates remain involved and the search is ongoing. A source close to the athletic director search told ESPN earlier Sunday that a hire had not been made.
Radakovich earned a business degree from Miami and began his athletic administration career there in 1983.
Cristobal on Friday confirmed Oregon's contract offer following the team's 38-10 loss to Utah in the Pac-12 championship game.
"Oregon's working on some stuff for me, and that's what I have right now and that's the extent of that conversation," Cristobal said Friday night. "If there's anything to report, I'd report it. I always have."
Cristobal recently traveled back to Miami to be with his ailing mother, Clara. Sources close to Cristobal told ESPN that family reasons would motivate Cristobal's move more than financial ones.