It has been claimed that Hart, who was dropped by Pellegrini earlier this month, could be loaned out in the mid-season transfer window.
Pellegrini also insists he is not looking to sign another keeper, therefore dismissing fresh reports linking the club with Stoke's Asmir Begovic.
Hart, after sitting out City's last five games, is poised to return for the midweek Champions League clash against Viktoria Plzen at the Etihad Stadium.
Pellegrini said: "There is a lot of news about six or seven goalkeepers that we want to buy but it is not true.
"Of course he stays. There is no chance that Joe Hart could go out of this squad in January."
Hart's situation continues to command much attention because he remains crucial to England's World Cup plans.
He has not played for City since a late error - one of a number of mistakes for club and country over the past year - proved costly in City's loss to Chelsea on October 27.
An encouraging display in England's friendly against Germany last week raised the prospect of a return but he remained on the bench for Sunday's 6-0 thrashing of Tottenham.
With qualification from Champions League Group D already assured, Pellegrini has promised Hart will get another chance against Plzen but has offered no long-term guarantees.
Costel Pantilimon has done little wrong since taking Hart's place and could be back in goal for Sunday's encounter with Swansea in the Barclays 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 was speaking at Eastlands at a pre-match press conference ahead of the Plzen fixture.
There is little riding on the contest with City having guaranteed a place in the last 16 with two games to spare.
But if results go their way, they could still supplant reigning champions Bayern at the top of the group and Pellegrini wants to finish the section with a flourish.
The Chilean, whose side beat the Czechs 3-0 in September and are in great goalscoring home form, said: "I think it is very important to win the group.
"It is not the most important thing, the most important thing is to qualify, but I think it is important to be at the top.
"It's also important to play well on Wednesday.
"We are not trying to score five or six goals every match here.
"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.
Pellegrini said: "Vincent started this week on some work with the whole squad. I think next week he could play.
"I think (Stevan) Jovetic, (David) Silva and (Jack) Rodwell need another week or 10 days more to be fit. They will not be involved on Wednesday or at the weekend."