The Argentinian suffered the injury in Manchester City's UEFA Champions League defeat to Barcelona last week, and manager Pellegrini revealed on Friday that he will be absent from both his side's home clash with Fulham on Saturday and the trip to Manchester United on Tuesday.
"Maybe next week Sergio will start working with the squad, but I don't think that he will be able to train for the whole week," he said.
"I think it's more likely that maybe towards the end of the week he can be with the squad and start training.
"It is possible he could be available for next weekend but we will have to wait and see."
Pellegrini also took time to dismiss speculation of a possible transfer that would see Aguero move to Barcelona.
"We cannot talk every week about players that are coming here to Manchester City and the players that are going out," the Chilean added.
"Aguero is a Manchester City player, he is very happy here and the club is very happy to have him."
Pellegrini confirmed that Stevan Jovetic is back in contention for the Fulham game, although Matija Nastasic remains unavailable, before warning his players that the Londoners will pose a stiff test, despite the fact they sit bottom of the Premier League.
"All the teams near the bottom, not only in the relegation zone but in the lower half of the table have to try to add points from somewhere," he said.
"Felix Magath's teams always play with a lot of intensity. I am sure we need to work hard during the game if we want to win.
"This is the start of a very important week and the most important game is Fulham because this is our next game.
"We know they are in a relegation position at the bottom of the table, but I repeat it doesn't mean it will be an easy match."
