Gay is turning down a salary of $8.8 million in order to hit free agency.
The 31-year-old veteran signed a two-year, $17 million deal with the Spurs last offseason, and the deal contained a player option on the second year.
During his lone season in San Antonio, Gay served in a reserve capacity for the first time in his 11-year NBA career. He appeared in 57 games during the 2017-18 campaign, averaging 11.5 points and 5.1 rebounds in a career-low 21.6 minutes per game.
The Spurs are now waiting for a decision from shooting guard Danny Green, who has a player option of $10 million.