"We're pushing everybody to start," Wilks told the NFL Network. "I've stated this several times: Sam Bradford is our starter. We gotta go out there with 11 guys and Sam's going to be the first guy out there. But everybody's fighting for a position, so I'm not going to hold [Rosen] back at all.
"I want guys competing, I want guys fighting for a starting job. Whoever ends up winning the position, that's who's going to end up playing."
Bradford, who signed a one-year, $20 million contract in March, appeared in just two games with the Minnesota Vikings in 2017. He went on injured reserve and had arthroscopic surgery in November before being activated as Case Keenum's backup during the postseason.
A former Heisman Trophy winner and top overall pick of the 2010 NFL Draft, Bradford has thrown for 19,049 yards with 101 touchdowns and 57 interceptions in 80 career contests with the then-St. Louis Rams, Philadelphia Eagles and Vikings.
Rosen, who was the 10th overall pick in the 2018 NFL Draft, passed for 9,301 yards and 59 touchdowns with 26 interceptions while playing in 30 games in three seasons as UCLA's starting quarterback.
This past season, Rosen passed for 3,754 yards and 26 touchdowns with 10 interceptions as UCLA finished with a disappointing 6-7 record. He did not play in the Bruins' 35-17 Cactus Bowl loss to Kansas State while recovering from a concussion.