Appearing on Arizona Sports 98.7 (h/t Darren Urban of Cardinals.com), general manager Steve Keim said Rosen's chance will come "when the time is right."
Keim elaborated on Arizona's stance regarding Rosen, noting rookies who play too early can be negatively affected by their experience.
"Some guys have played too early and it has crippled their career," he said. "I'm not going to name names, but I think a lot of us can think of certain players. Then there are guys who have come in and had success right away. But usually it's a rocky road."
The Cardinals are off to an 0-2 start and have scored a total of six points with Sam Bradford starting at quarterback.
Arizona's offense ranks last in yards per game (175.0), passing yards per game (114.0) and yards per attempt (4.0). Bradford's quarterback rating of 55.6 ranks last among all qualified players.
Rosen was selected by the Cardinals with the No. 10 overall pick in the 2018 NFL draft. The 21-year-old set a UCLA single-season record with 3,756 passing yards last year. He went 16-of-29 for 148 yards and one touchdown during the preseason.