A gamble on Carlo Ancelotti to become the next Manchester United manager took place on Wednesday.
Ignacio Camacho has ended speculation over his future by signing a new contract at Malaga.
Pellegrini has also played down speculation he might look to sign a new keeper during the mid-season transfer window.
Hart, the current England first choice, recently lost his place in the City side after a series of inconsistent displays and has sat out their last five games.
Pellegrini said: "There is a lot of news about six or seven goalkeepers that we want to buy but it is not true.
"There is no chance that Joe Hart could go out of this squad in January."
Hart has not played for City since a late error proved costly in City's loss to Chelsea on October 27.
He has been told he will return as Czech minnows Viktoria Plzen visit the Etihad Stadium in the Champions League on Wednesday night but Pellegrini has given no assurances about his long-term prospects.
Costel Pantilimon has done little wrong since taking Hart's place and could be back in goal for Sunday's clash 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 a press conference to preview the game against Plzen, which will be their penultimate fixture of group stage.
The pressure is now off with City having already secured their place in the knockout rounds but Pellegrini wants to finish the section with a flourish.
If results go their way, they could still supplant reigning champions Bayern at the top of Group D.
Pellegrini 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 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.
Pellegrini said: "Vincent started this week on some work with the whole squad. I think next week he could play."