Maicer Izturis finished 0-for-6 in Sunday's 13-inning loss to the Padres.
David Hernandez has allowed one run run since April 30.
Jesse Litsch told Sportsnet's Barry Davis that his shoulder infection has become "career threatening."
Garrett Jones doubled in Sunday's loss to the Tigers.
Alejandro De Aza went 2-for-5 as the White Sox finished off a sweep of the Cubs on Sunday.
Kosuke Fukudome is batting just .175/.286/.200 through 49 plate appearances this year for the White Sox.
Mike Adams (chest) was available on Sunday.
Austin Jackson (abdomen) is aiming to play in the Tigers' upcoming series against the Indians.