The player said on Twitter on Thursday: "Thank you for your messages. I broke my finger during the last international game, I will let you if I will be able to play Saturday."
The club are yet to confirm the nature of the injury but are not thought to be overly concerned about the problem.
Nasri came on as a 75th-minute substitute in France's goalless Euro 2012 qualifier in Romania on Tuesday.
However, the £24million signing from Arsenal last month remains in contention for the Latics clash, which will be his home debut for City should he feature.
The playmaker has already excited Blues fans with an impressive first run-out for his new club, setting up two goals for Edin Dzeko in a storming 5-1 victory at Tottenham just under two weeks ago.
Since then, City boss Roberto Mancini has further boosted his midfield with the transfer deadline-day capture of free agent Owen Hargreaves.
Mancini's move for the 30-year-old former England international - who was released by Manchester United earlier in the summer after an injury-blighted four-year spell at Old Trafford - came as a surprise to many at the end of a window in which the Blues once again flexed their considerable financial muscle.
The Italian coveted Daniele de Rossi of Roma and Real Madrid's Fernando Gago, but has revealed bringing City in line with UEFA's financial fair play regulations was the reason for the acquisition of Hargreaves.
Mancini said: "Gago is a player we liked a lot. We couldn't spend any more money also for the question of financial fair play.
"De Rossi is one of the best midfielders in the world but I don't believe he will ever leave Roma.
"So in midfield we signed Hargreaves, who was out of contract.''
Mancini's assistant David Platt added: "We needed a central midfield player but unfortunately in terms of players going out and bringing in transfer fees, a lot have gone out on loan, so fees haven't come in for them. You have to get creative."