Manager Joe Girardi said Robertson, on the disabled list with a strained left oblique is feeling better, and the Yankees are thinking about sending the reliever to Tampa along with injured left fielder Brett Gardner later this week.
They initially hoped Robertson would be able to return from his injury on Sunday -- after the minimum 15 days -- but that now appears out of the question.
"That's probably pushing it, because he's not going to pick up a baseball probably until Thursday," Girardi said of the right-hander. "That would be really pushing it."
Before hitting the DL, Robertson had two save opportunities following Mariano Rivera's season-ending right knee injury. The fill-in closer finished off a win over Tampa Bay on May 8 but blew the save and took the loss the next night, when he surrendered four Rays runs on three hits and a walk in two-thirds of an inning.