"Westlake (Ehlinger's high school) is a great program, but the two best quarterbacks to come out of there are Drew Brees and Nick Foles. Sam can stay down there in Texas," Mayfield said on SportsTalk1400.
"That'll stir the pot," he continued. "He doesn't like me and I hope he knows I don't like him either."
The two pivots met on the field just once in college, when the Sooners earned a 29-24 victory over the Longhorns in 2017. Mayfield was selected with the No. 1 overall pick in the NFL draft next year.
The Big 12 rivals met twice last season, with Texas emerging with a thrilling 48-45 win during the regular season and Oklahoma capturing the conference title by a score of 39-27 in December.