Shaw was suspended through the 2020 season - and potentially longer - on Friday after the league found that he bet on multiple contests this year.
The 27-year-old reportedly made a three-team parlay bet on Nov. 10 that included the Cardinals' Week 10 matchup against the Tampa Bay Buccaneers.
If his appeal is denied, Shaw may petition for reinstatement on or after Feb. 15, 2021, Purdum adds.
Shaw has yet to make his debut in Arizona. He signed a one-year contract with the NFC West club in March but was placed on injured reserve during the preseason due to a shoulder injury.