White Sox manager Pedro Grifol said Saturday that Jimenez (hamstring) could be reinstated off the injured list as soon as Monday, Daryl Van Schouwen of the Chicago Sun-Times reports.

Grifol noted that Jimenez is "up to 90 [percent] running, he's passed the test" when it comes to his left hamstring strain. Jimenez began his rehab assignment in the rookie-level Arizona Complex League on June 13, and across six outings he's gone 8-for-18 with one double, one home run and five RBI. Jimenez was one a five-game hitting streak and slashed .286/.359/.457 over his last 10 major-league games before the injury.