Cueto has yet to face hitters at the White Sox's extended spring training facility in Arizona but could be ready to throw live batting practice within the next few days, Daryl Van Schouwen of the Chicago Sun-Times reports.

Since Cueto didn't sign his minor-league deal with the White Sox until April 4, he's only about one week into his own version of spring training. The White Sox envision Cueto serving as rotation depth, so he'll likely need at least a couple of weeks to get adequately stretched out for starting duty before the team determines whether there's room for him on the big-league roster. Lucas Giolito (abdomen) was added to the injured list Tuesday, but Cueto looks to be a more logical candidate to replace Lance Lynn (knee), who is sidelined with a longer-term injury than Giolito.