Floyd has had a few throwing sessions over the past week as a part of his rehabilitation procedure. In what has been a disappointing season, the right-hander has been shut down twice due to elbow discomfort.
"There is (pain), but not on every throw," said Floyd, who is 9-9 with a 4.55 ERA this season. "I think the medication has worked well but it is still tender and still sore."
There is no timetable for Floyd's return to the roster and with only 32 days left in the baseball calendar, Floyd may indeed miss the rest of the regular season.
"First he has to throw out there without pain," manager Robin Ventura said. "Then you go from there. He still has a little bit of pain in (his elbow). I wouldn't be comfortable even setting a time for him to pitch right now."
The veteran pitcher is working at the end of a four-year contract. The White Sox hold a team option for 2013.