Sale, an American League All-Star selection the past two years, went on the disabled list on April 22 with a left flexor strain. He was 3-0 with a 2.30 ERA in four starts before the injury.
"He threw free and easy," White Sox manager Robin Ventura said after monitoring the bullpen session. "It's another step in the right direction. We'll continue to see how he is."
The White Sox have not listed any probable starter for the four-game series with the Yankees, which begins Thursday. Ventura did not rule out Sale starting one of the four.
"He could be," Ventura said. "It's too early to say."
Sale struck out 11 and allowed one hit in four scoreless innings Friday in a minor league rehab start with Triple-A Charlotte.
"It went well," White Sox pitching coach Don Cooper said of Sale's bullpen session. "Now we have to decide what to do and where to do it. It was nothing different than what we've seen before."
Cooper said there is no need "to stretch" Sale out in innings before he returns.
"Chris has always thrown strikes with all his pitches," Cooper said. "Touch and feel is more important."
With closer Matt Lindstrom going on the disabled list Tuesday with a left ankle injury, Ventura has not selected a replacement.
"We're not going to name a closer," Ventura said. We have options, guys who can do it. Even guys who are pitching in the eighth could go in the ninth. We have guys who can go multiple innings."
Lindstrom returned Tuesday to Chicago for most tests, including an MRI, on his ankle. He was injured fielding a bunt in the ninth inning Monday while attempting to field a bunt in the White Sox 7-6 victory over the Royals. Jake Petricka got the final two outs for his first career save. Lindstrom had all six White Sox saves before then.
"We don't know the full extent, but he wasn't walking very good," Ventura said. "He said it felt like something kicked him in the back of his ankle."