Rubio, 30, returned to Minnesota last season after being included in the Chris Paul trade. He averaged 8.6 points and 6.4 assists for the Timberwolves following a resurgent season with the Suns.
The Cavaliers recently lost longtime backup point guard Matthew Dellavedova after he signed a three-year deal with Melbourne United this month.
Rubio is on the last season of a three-year, $51 million contract.
Prince, 27, was acquired by Cleveland in a trade with the Brooklyn Nets this season. He averaged 10.1 points, 3.7 rebounds and 2.4 assists in 23.7 minutes per game.