The France international's progress after a knee injury lifts the club ahead of the first leg of their Champions League last-16 tie against Barcelona next Tuesday.
Nasri initially feared he could be out for up to eight weeks after being carried off on a stretcher in the Barclays Premier League win at Newcastle on January 12.
But he featured in a session for the first time as City trained at the Etihad Stadium ahead of their midweek clash with Sunderland.
While that game comes too soon, Saturday's FA Cup fifth-round tie against Chelsea could be an outside possibility, as it might for another recent injury victim in midfielder Javi Garcia.
Manager Manuel Pellegrini, speaking at a press conference, said: "Nasri and Javi Garcia started training today with the squad, we will see in the rest of the week if they can be fit for Saturday."
When asked specifically about whether Nasri could play against Barcelona, Pellegrini said: "We will see in the next few days, up until Saturday. I think there is a chance."
Nasri, 26, is also hopeful of an imminent return.
The player tweeted: "Happy to be back with the team, first full session cant wait to be back in the squad thank you for your support."
Nasri had been in fine form before suffering ligament damage in a controversial tackle from Mapou Yanga-Mbiwa.
The former Arsenal star's potential return is timely for City, coming as their momentum has just been slowed.
Title rivals Chelsea ended their 20-match unbeaten run last week before Norwich held them to a goalless draw at Carrow Road on Saturday.
Two other key players in top scorer Sergio Aguero and midfielder Fernandinho also missed those two fixtures through injury and, while making good progress, are not yet ready to return.
Asked if they could play against Barcelona, Pellegrini said: "I don't think so."
The Chelsea and Norwich games saw City fail to score in successive fixtures for the first time this season.
Prior to that they had been in fine goalscoring form, having taken their tally for the campaign to 115 with a 5-1 win at Tottenham, a result which also took them top of the table.
Pellegrini bemoaned his missing players and others not fully fit after the shut-outs, but he insists he was not making excuses.
The Chilean, speaking at a press conference to preview the Sunderland game, said: "It is not an excuse, I see a reality.
"In the same position we have three players, all strikers, who are not 100 per cent.
"And in another position we have Fernandinho and Javi Garcia out, it is just bad luck at this moment of the season. That is not an excuse for why we didn't win both games.
"It's not a weakness in our squad, but some bad luck to lose two or three players in the same positions."
The latest results saw City quickly surrender top spot but Pellegrini is hopeful the goals will soon start to flow again.
The 60-year-old said: "We need to start scoring again, and not only the strikers, because all of our players have been scoring goals.
"It's not normal to not score for two games in a row, but I hope in future this won't continue."