"Bobby, he told me he can go," Guillen said. "If he's not pitching in the game, he will throw a [side bullpen session]."
Jenks warmed up in the eighth inning but never got into the game.
Jenks last pitched in Detroit on Thursday afternoon, when he allowed a game-tying, two-out home run to Ryan Raburn in the White Sox eventual 6-4 win over the Tigers. He felt tightness in his back Friday, leading to Guillen using J.J. Putz in the closer's role on Saturday.
Guillen did not say in what role Jenks would have be used in if needed Monday. Guillen had said previously that Jenks would need an outing to work his way back into the closer's spot after the nagging back injury.