Barry back for Man City after international break, Richards a little longer
The midfielder had surgery on a groin/hernia problem which forced him out of England's Euro2012 campaign but is expected back for the champions when they travel to Stoke City on September 15.
"Gareth will also be ready after the international break," Mancini told the club's official website.
"He hasn't played any games for almost four months and he needs to build his fitness up, but he is training again and I don't see him being out for any longer than one month and hopefully, maybe just a couple of weeks."
Meanwhile, defender Micah Richards is still about a month away from returning as he continues to recover from an ankle injury he sustained whilst representing Team Great Britain at the Olympics.
"Micah's injury is more serious and he could be out a little longer, but having said that, with rest and the right treatment, we are hopeful he could be ready in about one month, which again would be great news," the City boss added.