Rodon (biceps) remains on a throwing program but manager Rick Renteria remains vague about the left-hander's progress, Daryl Van Schouwen of the Chicago Sun-Times reports.

In a question-and-answer exchange with reporters Tuesday, Renteria replied to three questions about Rodon with a variation of the same answer: "He continues to be on his throwing program, and he's doing well. He's progressing well." Rodon did not meet with the media when he was back in Chicago last week and has since returned to Arizona. The White Sox won't say if he's thrown off a mound. Once he's ready to take the mound, Rodon will need a few turns through a rotation to build up strength and innings. A best-case scenario has Rodon returning in early June.