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. 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 added: "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.
Last season's top scorer 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. Yaya Toure, Kolo Toure and back-up striker Abdul Razak are also missing for at least a month after joining up with Ivory Coast for the African Nations Cup.
It had been reported midfielder Yaya Toure needed treatment at a clinic for a cough and a fever while at a training camp in Abu Dhabi but his brother Kolo has said he is "back on his feet".
The defender added: "Yaya had a couple of days off. Apart from that, everything is going very well at the training camp and we are happy to be here."
With Aguero sidelined, controversial striker Mario Balotelli staked his case for a return to the starting line-up at Arsenal this weekend with two goals in a surprise appearance for the under-21s.
Balotelli, who was involved in a training ground bust-up with manager Roberto Mancini last week, was hoping to improve his match-fitness in a friendly against Blackburn at Platt Lane. The 22-year-old missed five games, four of them with a virus, before returning as a substitute in Saturday's FA Cup third-round win over Watford.