The qualifying offer means the Grizzlies have the right of first refusal should another team try to sign Gay, their longest-tenured player.
It also means the Grizzlies are apparently willing to see what the market holds for Gay, who can negotiate with other teams during the free agency signing period that starts Thursday.
The 6-foot-8 forward was second on the Grizzlies in scoring last season with 19.6 points per game. Gay, a four-year veteran, is considered a rising talent who could earn interest from other teams seeking a young, athletic scorer.
Gay's agent, Jeff Austin, says Gay is prepared for the free agency period.