The Argentine was forced off against Arsenal with a calf injury and Pellegrini is wary that, despite positive signs during his rehabilitation, his star striker could miss the entire of January.
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However, there was more positive news regarding Pablo Zabaleta, who picked up an injury against Leicester, with Pellegrini suggesting the full-back is likely to miss no more than two weeks.
"I think Pablo is not so big an injury," he continued. "Maybe he will be back soon. Maybe a week or two but the doctor will decide."
The City boss also confirmed that Micah Richards, Matija Nastasic and Stevan Jovetic will also miss Manchester City's game at Fulham this weekend.
Pellegrini's side travel to Craven Cottage just four points off league-leaders Arsenal following their 6-3 win over the Gunners at the Etihad Stadium.