Per NFL Network's Ian Rapoport, the Cardinals are "making a lot of noise" about trading up from the No. 15 pick.
After Carson Palmer retired in January, the Cardinals signed Sam Bradford to a one-year deal as his replacement.
The oft-injured Bradford is trying to rebuild his value in Arizona. The 30-year-old appeared in just two games last season with the Minnesota Vikings. He set an NFL record with a 71.6 completion percentage in 2016, which New Orleans Saints quarterback Drew Brees (72.0) subsequently broke last season.
The Cardinals are beginning their first season under head coach Steve Wilks. They missed the playoffs in each of the past two seasons under Bruce Arians after reaching the NFC Championship Game in 2015.