General manager Rick Hahn said Monday that the White Sox won't "rush" Cease to the big leagues, but noted the right-hander is "not too far away" from receiving a promotion from Triple-A Charlotte, Daryl Van Schouwen of the Chicago Sun-Times reports.

Service-time concerns are probably the main reason why Cease has yet to make his MLB debut, as the White Sox have already lost a key rotation piece in Carlos Rodon (elbow) for the season and own the sixth-worst starters' ERA (5.36 ERA) in baseball, despite Lucas Giolito's emergence as a bona fide ace. Cease has stumbled a bit over his last few turns at Triple-A, but his 4.10 ERA, 1.46 WHIP and 59:22 K:BB in 52.2 innings are still largely impressive after factoring in the enhanced power environment in the International League this season. Before giving Cease a long-awaited promotion, the White Sox may want to see him bounce back from his worst outing of the season Sunday, when he failed to escape the first inning while yielding two hits and three walks.