Cozart took batting practice on Tuesday with the team, which he hadn't done since Saturday. He was told to rest Sunday and Monday.
"We're trying not to rush back," Cozart said. "It felt great the first day I took BP and we came back Sunday, less than 24 hours later, it was a little sore from the day before. We decided to take it slow."
Cozart was optimistic that he could be back during this weekend's series vs. the Dodgers at Great American Ball Park.
"I don't have a set date," he said. "If I keep making progress, I wouldn't be surprised if it's, hopefully, this weekend."
Cool temperatures at Wrigley Field could throw a wrench into the optimism, however.
"This is the time of year when weather can change day to day," Reds manager Dusty Baker said. "It affects Cozart as much as anybody. It's harder to keep that oblique area loose and warm."