"It's probably not healing as quickly as I would like," Girardi said. 'I don't think that you can ever say, when you come from an injury like a broken hand, how long it's going to take. Maybe it's taking longer than we expected, but we didn't really put a time on it."
General manager Brian Cashman said on Friday that Granderson could be back with the Yankees by the end of July, and Girardi agreed that was a possibility.
"Once he starts hitting," Girardi said, "it'll go pretty quick."
Granderson injured his hand after being hit with a pitch on May 24 against the Rays, which was just his eighth game of the season after missing the first month and a half with a broken arm suffered in Spring Training.
He's batting .250 with a home run, an RBI, five runs and a stolen base in 28 at-bats this season.
Josh Vitale is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.