The Argentina international had to be substituted with a calf injury against Arsenal earlier in December but his projected comeback is earlier than initially expected.
The Argentine, who has scored 19 goals in all competitions this season, was forced off during a 6-3 win over Arsenal on Dec. 14. Pellegrini had initially feared his talisman might miss up to eight weeks but is now hopeful the forward will be available once again early in the new year.
"Sergio is doing his recovering from his calf injury," he told reporters. "I suppose that in January he will be OK."
The Chilean was speaking at a pre-match press conference ahead of his side's trip to Swansea City, and confirmed that Martin Demichelis, Stevan Jovetic and Micah Richards will also be absent alongside Aguero. Goalkeeper Joe Hart suffered a cut to his face during Saturday's 1-0 win over Crystal Palace but Pellegrini described it as "not dangerous," with the England No. 1 in the running to face the Swans.
The manager also declared Alvaro Negredo, Yaya Toure and Pablo Zabaleta available after all three were omitted from the starting XI against Palace.
"I think it was a fantastic month for us," the City boss said of the team's fine December form. "We played 10 games and won nine - and, in the Premier League we won six. It was very important for us to recover points with Arsenal and very important to finish the year in the position we wanted to be. To recover six points in a month is not a bad thing. Now, in the second half, we try to win it."
Questioned on transfer plans, meanwhile, Pellegrini replied: "For the moment we are not talking about that. We are always analyzing what we need [and] what we don't need. The possibility of the winter transfer window is for every club. We'll see what we are going to do in the next days."