Aguero could face longer spell on sidelines
Manchester City's Argentinian forward Sergio Aguero celebrates after scoring against Arsenal at the Etihad Stadium in Manchester on December 14, 2013
Pellegrini had previously said he expected Aguero to be out for up to four weeks after he suffered a calf injury in Saturday's 6-3 thrashing of Arsenal.
But there remains uncertainty as to the true extent of the problem and Pellegrini said it could be worse than first feared.
Pellegrini, speaking after City's 3-1 League Cup quarter-final win at Leicester on Tuesday, said: "I am not a doctor. It is very difficult.
"The doctor has said he has at least one month or eight weeks. We will see.
"I don't how many weeks but it will be at least one month. It is very difficult to know at this moment how many weeks it can be."
Aguero's absence for that length of time would be a major blow to City, with the 25-year-old having scored 19 goals already this season.
He had found the target again against Arsenal but then pulled up when under no pressure early in the second half.
Aguero is certain to miss the Christmas programme, which includes a home clash with Liverpool in the Premier League, and could also be out for both League Cup semi-final legs in January.
An extended lay-off could also make the Argentina international doubtful for City's Champions League last 16 tie against Barcelona in February.
There was more bad news on the injury front for Pellegrini as Argentine right-back Pablo Zabaleta suffered a hamstring injury early in the win at Leicester.
With Micah Richards already sidelined with a similar problem, City could now have difficulties in that position in the weeks ahead.
Pellegrini added: "Pablo has a problem with his hamstring. We will see tomorrow (Wednesday) how serious it is.
"It is the only bad thing of this game.
"Of course now we don't have a (right) full-back. Maybe we will have to see what we can do in that position."