The club can match any offer made during the free agency signing period to Gee, who averaged 10.6 points and 5.1 rebounds in 63 games - 31 starts- last season.
Gee was one of the Cavs' most improved players and general manager Chris Grant said keeping the former D-League player "is a priority for us." Gee began the season as a reserve but worked his way into the starting lineup.
Gee is expected to draw interest from other teams.
Also, the Cavs extended a $1 million qualifying offer to forward Luke Harangody. The team has not yet decided whether to make an offer to backup center Semih Erden.