The Argentine, who has 19 goals in 20 competitive games this season, has been out since December 14 with a calf problem while James Milner is also endorsed for England.
The Argentina international has not featured for City since its 6-3 win over Arsenal on December 14 because he picked up a calf injury.
In the striker's absence, Pellegrini's side has won five of its last six games - only failing to beat Blackburn Rovers in Saturday's FA Cup third-round tie.
Aguero is unavailable for Wednesday's League Cup semifinal first leg match with West Ham, but Pellegrini is optimistic the former Atletico Madrid man will return ahead of Premier League meetings with Tottenham and Chelsea to come at the end of the month.
"I think Sergio will be back during January. He's working, he is training," he said. "When all the players recover from their injuries it's good news. Especially an important player like Kun Aguero."
Stevan Jovetic, Jack Rodwell and Jesus Navas will also miss West Ham's visit because of injury, while Micah Richards will not feature, despite recovering from a hamstring problem.
"Richards can play but he is not in the squad because he must work a little more but he is not injured," Pellegrini said.
The Chilean also endorsed James Milner, after Theo Walcott was ruled out of the World Cup on Monday with a cruciate ligament injury.
"I can't tell Roy Hodgson which is the best choice [to replace Walcott]," he said. "I think that Milner is a very useful player. He is always playing here and for me, I trust a lot in him. For me, he is a very good player."