The Manchester City boss said the Argentine could be out for up to eight weeks — twice the initial prognosis — although Pablo Zabaleta will be back sooner than expected.
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 all of January.
"Aguero could be [out for] eight weeks, could be four," the City boss told reporters. "We will see the way he is working but he is improving every day."
However, there was more positive news regarding Pablo Zabaleta, who picked up an injury against Leicester, with Pellegrini suggesting the fullback 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 travels to Craven Cottage just four points off league leader Arsenal following a 6-3 win over the Gunners at the Etihad Stadium.