Citing a person with knowledge of the deal, the newspaper said guard Jose Calderon, forward Ed Davis and a second-round draft pick were shipped to Memphis, with the Grizzlies then sending Calderon to the Detroit Pistons in exchange for forwards Tayshaun Prince and Austin Daye.
The Grizzlies originally obtained Gay in 2006 shortly after he was taken by the Houston Rockets with the eighth overall choice in the NBA Draft. He sports career averages of 17.9 points and 5.9 rebounds per game.
Calderon, meanwhile, had recently expressed a desire leave the Raptors, for whom he has played his entire seven-year NBA career.
The Spain native -- who was set to become a free agent after this season -- has averaged 10.0 points and 7.2 assists over 525 career games with Toronto.
That deal allowed Memphis to unload $6 million in salary and avoid paying a $4 million NBA luxury tax this season.