Earlier this month, Peterson said he has been very impressed with Rosen, the No. 10 overall pick in this year's NFL Draft. However, Bradford signed a one-year, $20 million contract with the Cardinals in March and is the presumed starter.
Peterson told NFL Network recently that he agreed the veteran should get the starting nod.
"Well, right now I'd probably take Sam due to his experience," Peterson said. "Due to some of the records that he has in the league. Because when Sam is healthy and is on the field and has talent around him, he's a top-10 quarterback."
The 30-year-old Bradford has a lengthy injury history, appearing in only two games with the Minnesota Vikings in 2017. He has played 80 of a possible 112 regular-season games. If he can stay on the field, the former Heisman Trophy winner and No. 1 overall pick in 2010 is expected to be under center in Week 1.
"The biggest knock on Sam is just staying on the field," Peterson said. "I think we have a pretty good opportunity to keep him on the field because last year he really didn't have to fix anything, just cleaning up his knee. ... If he's on the field, we'll see where the chips stack and where they fall at the end of the season."
Rosen passed for 3,754 yards and 26 touchdowns with 10 interceptions in 2017 with UCLA. He posted career numbers of 9,301 yards passing with 59 touchdowns and 26 interceptions in 30 games.
The Cardinals finished 8-8 last season and are surrounded in the NFC West by teams with stars or budding stars at quarterback with the Los Angeles Rams (Jared Goff), San Francisco 49ers (Jimmy Garoppolo) and Seattle Seahawks (Russell Wilson).