Harrison (elbow) is scheduled to throw live batting practice Saturday and begin a rehab assignment July 31, Hunter Baumgardt of Fox Sports 920 Milwaukee reports.
Harrison has been on the injured list since just before the All-Star break due to elbow soreness, so he may only need one rehab start in the minors before re-entering Milwaukee's rotation. Assuming the left-hander avoids any setbacks, he could be back on the big-league mound during the first week of August.