Stanton was the backup to Andrew Luck at Indianapolis last season. The Cardinals also have John Skelton and Ryan Lindley on their roster of quarterbacks.
That, and contract issues, signaled Kolb might be released.
Kolb joined Arizona through a trade with the Philadelphia Eagles in July 2011.
He signed a contract with the Cardinals that was reported to be worth $63 million, including a $2 million roster bonus. When the sides were unable to restructure the contract, Kolb was cut.
Kolb played 15 games for Arizona over two seasons. He completed 194-of-319 passes for 1,082 yards and 11 touchdowns.
In his six-season career he's completed 449-of-755 passes for 5,206 yards and 28 touchdowns.