Rodwell, signed for £12 million from Everton in August, has not played since suffering the latest in a series of hamstring injuries on England Under-21 duty in October.
The 22-year-old had hoped to return to action before Christmas but suffered a setback and was ruled out until early in the new year.
The highly-rated Rodwell's time at Goodison Park was also blighted by such injuries and his hopes of playing at Euro 2012 or the London Olympics, after making an England debut in 2011, were dashed by them.
Mancini said: "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."
Rodwell, who also had a short spell out with a groin injury in September, has made just two starts and four substitute appearances since arriving at City.
City are hopeful their other long-term absentee Micah Richards, who required surgery after suffering a knee injury in October, will be back in action by the end of February, but Sergio Aguero could be out for several weeks following confirmation over the weekend that he tore his hamstring in the New Year's Day win over Stoke.
- Sports & Recreation