Rodwell, signed for £12million from Everton in August, has not played since suffering the latest in a series of hamstring injuries on England Under-21 duty in October.
Roberto Mancini: "He is getting better and we hope we can recover him in two or three weeks.
"He needs to start working with the group and he didn't do this until Thursday.
"I worry because when we bought him we thought he was a good player and then he had these problems with hamstrings.
"We hope we can improve this situation for him. He is young and has quality, he has everything to be a good midfielder."