Sidelined since July 20 with a left shoulder impingement, Drew has been hitting for the last several days.
He will start a Minor League rehab assignment for Class A Lowell on Friday and Saturday. Drew will work out with the Red Sox on Sunday and get a day off on Monday. Then he would play for Triple-A Pawtucket on Tuesday and Wednesday before returning to the Red Sox the next day.
Though Drew has had a tough season at the plate, his return might come at a good time. Josh Reddick, who has taken Drew's spot in the lineup, has struggled of late. In August, Reddick is hitting .226 with two homers and four RBIs.
Another player who is taking steps toward a return is reliever Bobby Jenks, who is in the midst of his third DL stint this season. Jenks threw a 24-pitch side session at the team's Spring Training complex in Fort Myers, Fla., on Monday. He will do so again on Wednesday and perhaps start a Minor League rehab assignment after that.