Rivera, 43, missed most of the 2012 season after tearing a knee ligament while fielding fly balls before a game at Kansas City in early May.
Uncertainty lingered over whether the likely future Hall of Famer would return to the Yankees next season to end his career while healthy, but Cashman said Rivera called him to indicate he'd like to play in 2013.
"Now [Rivera's agent] Fernando Cuza and I will work behind the scenes and do our jobs in making that happen," the GM said.
The 12-time all-star reliever is the all-time saves leader in MLB history with 608. He was only able to record five saves last season while posting a 2.16 ERA with a 1-1 record before going down with the knee injury.