Hart was dropped earlier this month following a number of high-profile blunders, but he will start Wednesday's Champions clash against Viktoria Plzen at the Etihad.
City have been linked with Stoke goalkeeper Asmir Begovic, with suggestions that Hart could move on loan in the opposite direction, but Pellegrini insists the England player will remain at the club.
"There is a lot of news about six or seven goalkeepers that we want to buy but it is not true," said the Chilean.
"There is no chance that Joe Hart could go out of this squad in January."
Hart has sat out City's last five games since his late mix-up with Matija Nastasic led to Fernando Torres' winner in the 2-1 defeat at Chelsea.
But England boss Roy Hodgson still views Hart as his first choice keeper and he showed glimpses of his best form in last week's 1-0 defeat by Germany.
Costel Pantilimon has done little wrong since taking Hart's place at City and could be back in goal for Sunday's clash with Swansea in the Premier League.
Pellegrini said: "I think that is a question for next Saturday.
"When we start the next game of the Premier League we will talk about who will start playing.
"The important thing for Joe is that he will play tomorrow and we hope he will have a very good performance."
Pellegrini's immediate focus is on the game against Plzen, and although City are already guaranteed a place in the last 16 they still have a chance of overhauling Bayern Munich to finish top of Group D.
"I think it is very important to win the group," Pellegrini said.
"It is not the most important thing, the most important thing is to qualify, but it is very important to play well also.
"The most important thing is to win and then we will see what happens."
Captain Vincent Kompany trained with the squad ahead of the game but is not yet ready to return to action after a thigh injury.
Kompany has been sidelined for the past few weeks after picking up the problem in a 3-1 win over Everton last month.
Pellegrini said: "Vincent started this week on some work with the whole squad. I think next week he could play."