The Cardinals have been shopping the No. 10 overall pick in the 2018 NFL Draft this off-season. Arizona selected Oklahoma quarterback Kyler Murray with the No. 1 overall pick in the 2019 NFL Draft on Thursday in Nashville.
The Dolphins have been "doing work" on Rosen for weeks after it was clear he was available via trade. Rosen was previously linked to the New York Giants and Washington Redskins, before both teams selected quarterbacks in Thursday's first round.
But the price for Rosen is unclear. Cardinals general manager Steve Keim told NFL Network that the team give Rosen away.
"I'm not giving up Josh for less than he's worth," Keim said. "He's a really good player. He's been amazing throughout this process, and I have nothing but good things to say about him. Quarterback's the most important position in the game, and without one, you're screwed -- so you'd better have more than one. Trust me, I know."
"Four years ago we went into a playoff game with our fourth stringer because our other quarterbacks got hurt, and it wasn't fun. So yeah, people might think it would be awkward to have them both, but I'm not worried about that at all. I have no reason to give Josh away."
Rosen, 22, completed 55.2 percent of his throws for 2,278 yards, 11 touchdowns and 14 interceptions in 14 games last season. The Dolphins were interested in the former UCLA quarterback during last year's draft, but were unable to trade up in the draft order to add him to their roster.