Gay averages 17.2 points and 5.9 rebounds.
Jazz forward DeMarre Carroll, who was Gay's teammate with the Grizzlies, said he would call Gay on Wednesday night to wish him well.
"I know it's kind of hard to leave a team where you've got them fourth in the playoffs and you go to a team that's probably not even going to make the playoffs," Carroll said. "The only thing positive you could take from it is a new situation, a new opportunity."
Entering Wednesday, the Grizzlies were 29-15 and in second place in the Southwest Division. Two years ago, Gay underwent midseason shoulder surgery. The Grizzlies went on to earn a playoff berth and topple the top-seeded San Antonio Spurs in the first round.
"I think ever since he got hurt and they made the playoffs," Carroll said, "they probably wanted to see if he could coexist. With he and Zach [Randolph] both being stars on the team, I guess they felt it was great timing to go a different way."
The Jazz, who have eight players with expiring contracts, are expected to be a player at the trade deadline. They were rumored to be interested in Calderon.
Jazz guard Gordon Hayward sat out for the second straight game due to a sprained right shoulder suffered Saturday against the Indiana Pacers. He is listed as day-to-day, and the Jazz have not targeted a day for his return.
"We want to be smart," coach Tyrone Corbin said. "We don't want to get him back and get him hurt again. We want to make sure he's well when he gets back. We need him to be healthy for the rest of the year for us. ... So as bad as I want him back in the lineup, we have to do the smart thing and the right thing by him."
Jeremy Evans is just waiting for news. After the Rising Stars challenge roster for All-Star weekend did not include any Jazz players, the springy 6-foot-9 forward remains the Jazz's best chance for representation in Houston.
The defending Slam Dunk champion said he expects to hear whether he is invited on Feb. 7 or 8, and that he will "probably" return to the contest if invited.
Many times defending champions, such as Blake Griffin, have opted not to defend their crown.
"You've got to top what you did before," Evans said. "... It still could be tough."
Evans has averaged 6.1 minutes in 20 appearances this season. He is 9 for 19 from the field and has pulled down 27 rebounds.
Evans said he is not worried about getting pigeon-holed as a dunker.
"I know what I can do," he said. "Other people won't know what I can do until I show them or they have their own opinion. If I seen someone on the court and that's all they ever did, that's what I'd pin them as, too. It just has to be shown."
At Paul Millsap
Welcome one more Jazz player to the land of ill-advised self-portraits and Bible verses. Paul Millsap joined social media platform Twitter on Wednesday, assuming the username @PaulMillsap_25 and, among his first posts, asking teammate and prolific tweeter Mo Williams to help him recruit more followers.
Carroll, another Jazz player to embrace Twitter, said he told Millsap to, "Watch what you say on there."
"Everybody will follow you," Carroll said he told Millsap. "Even people you think don't follow you, they're following you. The biggest thing on Twitter is be sure to tweet positive."