The 21-year-old has made six appearances in all competitions for the Premier League champions since moving from Everton for £12 million due to a succession of hamstring problems
The 21-year-old has only managed to make six appearances for Manchester City this season after his £12 million move from Everton in the summer.
Mancini hopes to have Rodwell, who has two England caps to his name, back in action soon, and insists that the midfielder has the ability to be a success at the Etihad Stadium.
"He's getting better and we hope we can maybe recover him in two or three weeks," the Italian told reporters.
"He needs to start to work with the group but he didn't do this until [last] Thursday.
"I'm worried because when we bought him we thought that he was a good player and then he has these problems with his hamstrings.
"We hope we can improve this situation for him because he's young, he's got quality, he has everything to have a good career."