The Argentina international had to be substituted with a calf injury against Arsenal earlier in December but his projected comeback is earlier than initially feared
The Argentine, who has scored 19 goals in all competitions so far this season, was forced off during December’s 6-3 win over Arsenal.
Pellegrini had initially feared his talisman might miss as much as 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."
|MAN CITY LATEST
|19/5||Alvaro Negredo is 19/5 with BetVictor to score the first goal in Swansea City v Manchester City|
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 added of their 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 analysing 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."