According to manager Bobby Valentine, Graham told Bailey he can start throwing next week.
When Bailey underwent surgery, the assumption was that he'd be out at least until around the All-Star break.
That could still be the case, but don't be surprised if Bailey at least tries to push the envelope.
"Boy, he's been working," said Valentine. "He's one of those guys I'm sure we're going to have to hold him back and proceed in a conservative effort."
Left fielder Carl Crawford (sprained ulnar collateral ligament in his left elbow) is also making progress, and he could start swinging the bat around the time the Red Sox start their next homestand on May 25.
The key for Crawford is when he will be able to start throwing.