Injured White Sox pitcher Chris Sale still doesn’t have a timetable for his return. But after throwing a 60-pitch simulated game Saturday, he might return during the Sox’ four-game series with the New York Yankees that begins May 22.

Sox bench coach Mark Parent, who served as the team’s manager Saturday while Robin Ventura attended his daughter’s college graduation, indicated Sale is eying that series for a possible return. A schedule hasn’t been set.

Sale, who was put on the 15-day disabled list retroactive to April 18 with a strained left flexor, threw four simulated innings, using all of his pitches in the middle two. After taking it easy in the first inning, Sale said he didn’t hold back in the latter three.

Sale said he was encouraged by the session. Indications are that he will make two rehab starts before returning to the Sox, though his preference would be one start so he could get back sooner.

“There’s going to have to be a meeting taking place,” Sale said. “We are going to have to talk about this. I would think that the next step would be a rehab start for me anyways.”

After feeling discomfort in his pitching arm, the left-hander had an MRI exam, which revealed no structural damage.

“Since the MRI, there’s really been zero concern on my end just because I know that it’s all muscular,” Sale said.

“But there is nothing — ligaments, tendons — nothing like that, so there was never a doubt in my mind. But it was a little slower process than I anticipated.”

Bullpen shuffle

The Sox purchased the contract of Frank Francisco from Class AAA Charlotte and designated Maikel Cleto for assignment.

Francisco spent time in the Sox’ minor league system before being part of the Carl Everett trade in 2003.

The 34-year-old Francisco ­allowed one run (unearned) in eight innings with Charlotte, and it came in his first game of the season. The Sox signed the nine-year major-league veteran to a minor-league deal April 14. He has a 3.93 career ERA.

In 13 relief appearances for the Sox this season, the 25-year-old Cleto has a 5.14 ERA.

Keeping continuity

Parent has been the interim manager before, and he preached continuity regarding his decision-making.

“I don’t try to stray too far from the way Robin usually does things and the things he likes to do, keep a certain continuity,” Parent said. “But there are some times when I’d rather do things that he doesn’t do.”

Email: sgruen@suntimes.com

Twitter: @SethGruen