The Serbian was stretchered off the pitch during Saturday's Asia Trophy final in Hong Kong which saw the Chilean pick up his first piece of silverware as the new City manager.
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But when asked if injury meant Pellegrini needed to act in the transfer market again, the Chilean told reporters: "It doesn't depend on just one thing.
"I said [before] that we could do something else before the Premier League starts but maybe we stay with the same squad. At the moment we aren't that concerned about that but I'm very happy with the squad we have."
City have been swift to spend almost £100 million so far this window, bringing Jesus Navas, Fernandinho, Alvaro Negredo and Stevan Jovetic to the club.
Real Madrid defender Pepe has been continually linked with a move to City this summer, although Madrid are believed to be determined to rebuff all bids for the Portugal international.