The Bruins left spring practice without naming a starter. Mora said that Mike Fafaul, Jerry Neuheisel, Josh Rosen and Asiantii Woulard will compete for the job during fall training camp.
That competition between two or more quarterbacks could continue past the first game.
"Heck, we might go three games and not know who the starter is," Mora said. "We could use the first three games to see where we are at quarterback. As we go, we'll get a better feel for our football team."
Mora said such a scenario is "only a possibility." UCLA has not sorted through quarterbacks since Brett Hundley won the job in 2012.
Mora said he has never entered a season without knowing who would play quarterback