White Sox's Mike Clevinger: Needs another rehab start

White Sox manager Pedro Grifol said Wednesday that Clevinger (elbow) will make another rehab start with Triple-A Charlotte, Vinnie Duber of AllCHGO.comreports.

The veteran right-hander threw 71 pitchers over 4.2 innings during his third rehab outing Sunday, and he'll continue building up his workload at Triple-A. Assuming that next outing goes well, Clevinger could step into Chicago's rotation during the first week of July.