White Sox manager Pedro Grifol said that Jimenez (adductor) could try to do some running Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Jimenez is missing a third straight start Wednesday against Atlanta after he suffered a left adductor injury Sunday. Grifol noted that the team hasn't made a roster move with Jimenez yet because there's a "possibility" the designated hitter could be ready to play this weekend in Kansas City. While Jimenez seems to have shown improvement since suffering the injury Sunday, Grifol seems less optimistic now about the slugger avoiding the IL than he did earlier this week. Gavin Sheets has been filling in at DH with Jimenez sidelined.