Crabtree's agent told UPI his client and the Cardinals didn't agree to terms on a contract.
The 31-year-old wide receiver had 607 yards and three touchdowns last season with the Baltimore Ravens. The No. 10 overall pick in the 2009 NFL Draft signed a three-year contract with the Ravens last off-season.
Crabtree had at least eight touchdowns in each of his three previous seasons with the Oakland Raiders before signing with the Ravens. He has missed just two games since the start of the 2014 season.
Arizona released its first official depth chart Friday. Larry Fitzgerald, Kevin White and Christian Kirk were listed as the starting wide receivers. Andy Isabella, Damiere Byrd, Chad Williams, KeeSean Johnson, Hakeem Butler, Isaac Zico, Trent Sherfield, Pharoh Cooper and A.J. Richardson were listed as reserves.
The Cardinals host the Los Angeles Chargers in their first preseason game at 10 p.m. EDT on Thursday at State Farm Stadium in Glendale, Ariz.