Peterson, 32, would be owed a $750,000 bonus on Friday, the third day of the league year, if he were still on the team.
The source said Peterson could re-sign with the Cardinals at a later date.
Peterson played in four games for the New Orleans Saints and six games for the Cardinals last season.
He had games of 134 and 159 yards with the Cardinals but otherwise totaled 155 yards in the four other games before suffering a season-ending neck injury in Week 12.
Peterson told ESPN's Josina Anderson on Monday that the Cardinals doctor told him "my neck is completely healed" after reviewing his scans. Peterson said, "I'm still looking forward to playing next season."
Peterson has 99 rushing touchdowns, tied with Barry Sanders for ninth all time. He has rushed for 12,276 yards, 12th on the all-time list, and is just 4 yards from passing Marshall Faulk for 11th place. He is the Minnesota Vikings' all-time leading rusher, gaining 11,747 yards in his 10 seasons with the team.
A seven-time Pro Bowl selection, he was the NFL's Offensive Rookie of the Year in 2007 and won the MVP award in 2012 when he rushed for a single-season career-best 2,097 yards.