Cincinnati placed the left-hander on the 10-day DL April 21, retroactive to April 19, after an appearance April 18 against Baltimore.
"What we do is listen to his body and we will define his next bullpen based on how he feels as he continues to play catch and as he exercises. He has not been shut down from throwing," Price said. "We're just going to give him an extra day or two just to make sure he's OK before he takes the mound the next time."
Cingrani last threw a 15-pitch bullpen on Tuesday. He got off to a strong start to 2017 in his five relief appearances, allowing one earned run in 4 2/3 innings with five strikeouts.
Chris Biderman is a contributor to MLB.com based in San Francisco who covered the Reds on Friday.