Girardi indicated a few days ago in Miami that Ellsbury wasn't where the team wanted him to be physically, and that it would be tough to have him back in the Majors by the end of June.
But Thursday, Girardi said Ellsbury is running again and that the team is encouraged by his progress.
"It appears that instead of maybe sending him to Tampa [Fla.] to work a few days down there before he plays in games, we'll just do most of it here," Girardi said. "He feels good ... he's not behind. We're happy with where he's at, and we're hoping to get him back pretty soon here."
Before he went on the disabled list, Ellsbury was hitting .324 with 14 stolen bases and six RBIs in 37 games.
Ellsbury said he talks to Girardi every day to update him on his progress. The outfielder added that the reason why he didn't go to the Yankees' complex in Tampa before he plays Minor League games is because of how much progress he's made with trainers.
"We figured, 'Hey, we might as well continue to make really good progress before I come back,''' Ellsbury said. "A rehab assignment would be when I'm ready to go down there. It wouldn't be before that. Do the stuff like I'm doing now -- it would be when I'm ready. Then I'd go."
He added that he's pushing himself as hard as he can each day, but he understands the importance of not returning to the field until he's fully certain that his knee is ready.
"Obviously I want to be out there. I'm working hard as I can to get back as soon as possible. We mentioned that six-week time frame, and [we're] working hard to cut it down each day," Ellsbury said. "Like Joe said, we're ahead of schedule, we're making good progress each day, and that's really all I can do."
Grace Raynor is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.