Gee was reportedly set to be a candidate to come out the bullpen before Zack Wheeler was lost for the year following Tommy John surgery to repair the ulnar collateral ligament and the flexor pronator tendon in his right elbow.
Gee, 28, went 7-8 with a 4.00 ERA in 22 starts for the Mets in 2014, missing almost two months because of strained back muscle. He put together the best season of his career with a 3.62 ERA in 199 innings during the 2013 campaign.
Gee had said that the trade rumors over the offseason did not effect his preparation in getting ready for the season.
New York has plenty of available candidates for the rotation, including top prospect Noah Syndergaard, and there could be a market for Gee's services.
The veteran right-hander is the Mets' control through the 2016 season and is set to make $5.3 million this season.
To this point, Dillon Gee has not been officially named as the fifth starter, further fueling speculation that he could be on the move.