City are still to learn the full extent of Aguero's calf injury, but such a lay-off could make him doubtful for the first leg of the Champions League clash against Barcelona.
City host the Catalan giants in the last 16 of Europe's elite competition in nine weeks' time, on February 18, before travelling the Nou Camp the following month.
The influential Aguero, who has scored 19 goals this season, limped off during City's 6-3 thrashing of Arsenal in the Barclays Premier League last weekend.
Pellegrini had previously said he expected the player to be out for at least a month, but back for the Champions League tie.
But if he is to be sidelined for closer to two months there may not be time for him to recover match fitness to face Barcelona.
Pellegrini, speaking after his side's Capital One Cup quarter-final win at Leicester, 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."
It therefore seems certain that Aguero will miss the Christmas programme, which includes a home clash with Liverpool in the Premier League on Boxing Day.
He could also be doubtful for both legs of City's Capital One Cup semi-final in January, a month that also includes Premier League games against Newcastle and Tottenham.
In addition, City also host title rivals Chelsea in the first week of February - another crucial game he could miss.