Yankees manager Joe Girardi said that Gardner will take batting practice on Wednesday and play in another extended spring game on Thursday.
If Gardner does not return for the Mets series, New York's visit to Atlanta from June 11-13 appears likely.
"We'll probably play him a few days in a row [and] just have to see how he does," Girardi said. "[The Mets series is] possible, but we'll just have to see how it goes."
Gardner has not appeared in a Major League game since April 17 due to a right elbow strain, which he aggravated on a Minor League rehabilitation assignment last month.