Pellegrini today said "We have some problems during the week with Samir Nasri. He has a calf injury so he will not be fit for the next game. He will be out for around three weeks or a month. Before that is difficult. All the rest of the team are fit."
A minimum of three weeks means he not only misses Arsenal on Sunday but also Chelsea on the 31st. City have five fixtures between now and an away trip to the Britannia on February 11th.
With Yaya missing out on the first leg against Barca (serving his third and final suspension for the red card against CSKA), it seems almost critical that Nasri be fit for that come February 24th -- so cross your fingers for a proper recovery in the predicted time frame.