Kim (elbow) will begin a rehab assignment at Triple-A Memphis on Thursday, Jeff Jones of the Belleville News-Democrat reports.
Kim has been sidelined since Aug. 8 as he deals with left elbow inflammation, but he's expected to throw 35-40 pitches during his first rehab appearance Thursday. Manager Mike Shildt said that the team hopes to build the southpaw back up to a starter's workload before he's activated, but he could return before he's back to his full pitch count if the Cardinals encounter any more injuries within their pitching staff.