Rodon is scheduled for Tommy John surgery to replace the ligament in his left elbow on Wednesday in Los Angeles. The left-hander started on Opening Day and made six more appearances before he was placed on the injured list on May 2 with elbow inflammation.
"Given that he has yet to undergo the surgery, it's still too early to give you a precise timeline in terms of his potential return," general manager Rick Hahn said. "However, in general, given the timing of the surgery, it is reasonable to expect Carlos to be able to rejoin us during the second half of the 2020 season."
Rodon was selected by Chicago with the No. 3 pick in the 2014 amateur draft. He has shown flashes of brilliance since breaking into the majors in 2015, going 5-0 with a 1.84 ERA during one stretch last year, but he has struggled with injuries.
Rodon missed the first three months of the 2017 season because of left biceps and shoulder inflammation. He had shoulder surgery that September, and the resulting rehab pushed back the start of his 2018 season.
"I think he is at peace with it in terms of the road ahead of him," Hahn said. "He knows it's not going to be, necessarily, an easy rehab, but at the same time, it's one that has a very, very high likelihood of success and one that should put him in a position to continue on and have a very, very promising career once he returns."
Jones had surgery Monday to repair a flexor mass tear in his right forearm. The 33-year-old right-hander also has been hampered by injuries since he had a 2.29 ERA in 71 appearances in 2016.
While Rodon and Jones have been ruled out for the year, top prospect Eloy Jimenez could return to the White Sox before their seven-game trip begins next week. Hahn said Jimenez will begin a rehab assignment with Triple-A Charlotte on Tuesday.
The 22-year-old Jimenez has been sidelined by a high right ankle sprain since he crashed into the wall in left during a 12-11 victory over Detroit on April 26. He is batting .241 with three homers and eight RBIs in 21 games.
"He's been looking very good," manager Rick Renteria said. "All the stuff that he's been doing both here and then on the road. He's going to be heading out and put himself back in game-type situations, and hopefully he'll be going through that in a positive way and be able to rejoin us."
The injury trouble for the White Sox extends into their highly regarded minor league system.
Hahn said outfielder Micker Adolfo will have arthroscopic surgery on his right elbow Tuesday but is expected to be ready for the start of next season.
"This is an unfortunate side effect sometimes of Tommy John in terms of the scar tissue buildup as well as issues that develop with the nerve," Hahn said. "Both of these are highly fixable, so we remain very optimistic on his full recovery and returning to us without restriction."
Hahn said Zack Collins is asymptomatic after dealing with a concussion and will enter the return-to-play protocol with Charlotte on Tuesday. The catcher was selected by Chicago with the 10th pick in the 2016 amateur draft.