Sergio Aguero will resume training with Manchester City's first-team squad on Friday and could be involved against Stoke City the following day.
The 24-year-old Argentina striker has been out since injuring his knee in City's opening game of the season.
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“Today is the first training that we have together after the international break. I am sure some of the players are tired. But we do not have time to recover”
"We will try this morning with Sergio," Mancini said. "After we try, we will decide. He is getting better."
When asked if he could be involved at the Britannia Stadium on Saturday, the Italian added: "Maybe."
Fellow forward Mario Balotelli has been cleared to play if needed after undergoing laser eye surgery during the international break.
The Italian had had difficulty wearing his contact lenses after being affected by conjunctivitis.
Mancini said: "Mario is OK. Mario now sees everything."
England midfielder Gareth Barry is close to returning after overcoming the abdominal problem that kept him out of Euro 2012 but defender Micah Richards remains sidelined with an ankle injury.
"Gareth hasn't played any games for almost four months and he needs to build his fitness up," said Mancini.
"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.
"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."
Aguero at Manchester City
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Mancini reported no new injury problems with players returning to the club from international duty, including three of the club's transfer deadline day signings - defender's Maicon and Matija Nastasic and midfielder Javi Garcia.
Those three, along with winger Scott Sinclair are in competition to make their debut for the club on Saturday.
"We don't have any players with injuries they are all OK," said Mancini. "Garcia is OK, Maicon the same. Nastasic was here yesterday for the first session but they are OK.
"Today is the first training that we have together after the international break. I want to wait until after this training session and then decide. I am sure some of the players are tired. But we do not have time to recover."