On Wednesday, Gardner underwent an MRI exam on his injured right elbow that revealed a healed muscle, although the left fielder still feels stiffness, likely from a bone bruise, according to manager Joe Girardi.
"He will still go to Tampa for treatment, working out his legs and stuff," Girardi said, "but our hope is he will start hitting off a tee on Monday."
Robertson is eligible to be activated from the 15-day disabled list on Sunday, but a return that early is out of the question. Girardi said the right-hander is targeting a return during the Yankees' June 1-3 series in Detroit.
Righty Rafael Soriano is the Yankees' closer in the interim, and Girardi would not say how he will arrange the back end of his bullpen once Robertson returns.
"Here's my prayer: Let's just get Robby back," Girardi said. "Let's just get him back to where he's comfortable and get him in a game before we start making official decisions."