Mending a strained right oblique, Granderson resumed swinging a bat and running the bases on Saturday while also throwing, saying he continues to feel some tightness but only minor discomfort.
"I'm 50-50 right now," Granderson said. "The way everything felt today was a good sign, another step forward. Hopefully everything continues the same way."
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Granderson said that he believes he may be able to get in a Grapefruit League game on Monday against the Rays at George M. Steinbrenner Field.
The center fielder suffered the injury on Tuesday while taking batting practice in Sarasota, Fla., at the spring home of the Orioles. Yankees general manager Brian Cashman indicated that the team may wait until next Wednesday's workout day at Yankee Stadium to decide if Granderson should be placed retroactively on the disabled list.
That would permit him to be activated for the April 6 game against the Twins in New York.
"That would be their call," Granderson said. "I feel like everything is fine in terms of avoiding the DL."