Putnam, who had season-ending surgery last Aug. 5 to remove bone fragments from his right elbow, started this campaign with nine strikeouts over 8 2/3 innings in absolute dominant fashion. But the right-hander left Saturday's contest against the Indians with right elbow tenderness after walking Carlos Santana.
At this point, Putnam considers himself day to day.
"We don't have a lot of concrete information right now," said Putnam prior to Monday's series opener with the Royals. "I'm going to do everything in my power to help [White Sox head athletic trainer] Herm [Schneider] and the medical staff avoid any sort of DL stint and any significant time missed, but we're really day to day right now.
"I'm going to try to give it a day to cool down a little bit, but that doesn't mean I'm necessarily unavailable. I'm just going to try to save some bullets as best I can."
This elbow malady came out of nowhere according to Putnam, who had been feeling pretty good.
"But it's a familiar feeling," Putnam said. "I know what to look for, and I know my body better than anybody.
"We've had very preliminary sort of scans and stuff, like an X-ray, and there's nothing significant there. There's no structural damage, so we're just going to give it a chance to calm down a little bit and hopefully be ready to go."
A decision would need to be made in the next couple of days regarding Putnam's status so as not to leave the bullpen short-handed if he can't go.
Rodon has been in Chicago for a few days and played catch from a couple of different distances Monday, with pitching coach Don Cooper watching.
Rodon declined to talk to the media, stating through a media relations representative he didn't want to be a distraction to the team. He is making progress in his throwing program for left biceps bursitis, based in Arizona, but to date he has not thrown off the mound.
"I just came out to watch him today. I hadn't seen him throw since Spring Training," Cooper said. "I'm not sure what the sort of schedule is for him. The ball looked fine. Listen, to a large degree what did he do? He played catch. But he played firm catch and he looked OK."
"Tough for me to give you a timeframe," White Sox manager Rick Renteria said. "His visit was just to make sure everything is moving in the right direction. It is. He's going to continue his program."
Cooper admitted Rodon is frustrated, wanting get through all of it. But as general manager Rick Hahn said Friday, no timetable can be set for Rodon's return until he gets on the mound.
"Well, I mean we've already taken a lot of caution," Cooper said. "He's important to us now and in the future. We wouldn't rush with him or anybody."