Jennings was placed on the 15-day disabled list on June 7, retroactive to June 5. He had a 2.70 ERA through April, but after giving up 14 earned runs in 11 2/3 innings in May, he headed to the DL with a 7.83 ERA.
Still, having him back will give manager Robin Ventura some flexibility out of his bullpen.
Ventura said that Zach Duke, the only lefty in the bullpen, has been more limited to lefty-on-lefty situations rather than full innings with Jennings out.
The White Sox could also be close to getting Matt Albers back in the bullpen. Albers pitched in four games before fracturing a finger in the team's April fracas with the Royals. Albers had surgery on the finger and was expected to miss six to eight weeks.
"We've been getting through it," Ventura said of the injuries. "You have these guys, they had roles, and you were counting on them, especially with Albers. ... It wasn't a baseball injury [from] him playing. It was a freak accident. It'll be nice to see where he's at tomorrow, going out there to compete and just see what he's got, and then we'll decide after that. "
Ventura also said that Nate Jones, who missed most of 2014 after undergoing back surgery and Tommy John surgery, is progressing well.
"He's been out in front of [the timeline] and you're happy with that, but I don't think we really are necessarily going to push it to see if he can set some sort of record of getting back," Ventura said. "You want to make sure he's healthy and go from there but so far things have been great for him."
Betsy Helfand is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.