After a workout at the Yankees' Minor League complex on Monday, Granderson will join Double-A Trenton on Tuesday.
Out since May 24 with a broken left pinky, Granderson went 2-for-13 with a walk and four strikeouts in four games with the Tampa Yankees against the Charlotte Stone Crabs. The 32-year-old outfielder said his timing at the plate is "getting better," and he was glad to hear Girardi's suggestion that he'll be taking his at-bats in the Majors fairly soon.
"I'd love to. Hopefully things continue to move well and progress the way that we all hope they will," Granderson said. "[If I] continue to play and feel good, it's a possibility. I'm glad that they're eager to get me back, and I'm excited to get back sooner than later."
On Sunday, Granderson struck out swinging, grounded out to the first baseman and hit a flyout to deep center field while facing Charlotte lefty Jacob Partridge. He faced right-hander Lenny Linsky in the seventh and went down swinging on four pitches.
Granderson did get one taste of the Majors in his latest Minor League rehab outing, as the Rays' Florida State League affiliate utilized a defensive shift against the lefty hitter.
"That's kind of [Tampa Bay's] motto -- definitely on the top -- so it must be all the way down," he said. "It's interesting to see it, for me mentally to go up there and just not try to change too much. As funny as it sounds, I'm actually glad they did it so it's not the first time I'll see it once I do happen to return, whenever that day comes. It won't shock me when that day comes."
• Alex Rodriguez went through another light workout at Steinbrenner Field on Sunday afternoon. The Yankees' third baseman was seen hitting in the batting cages in the bowels of Steinbrenner Field, playing catch on the field and fielding about 15 grounders hit directly at him on the outfield grass.
General manager Brian Cashman has said that Rodriguez, whose strained left quadriceps has been the subject of much debate lately, should be ready Thursday for a simulated game or a Minor League rehab outing. Rodriguez did not stop to speak with reporters as he left Steinbrenner Field.
Adam Berry is a reporter for MLB.com. Follow him on Twitter at @adamdberry. This story was not subject to the approval of Major League Baseball or its clubs.