Reports on Tuesday suggested Hart could be loaned to Stoke City, with Pellegrini hoping to use the England keeper as a makeweight to sign Asmir Begovic.
Hart has already been confirmed to start Wednesday night's UEFA Champions League fixture with Viktoria Plzen and Pellegrini ruled out the suggestion Hart was on his way out.
"There is a lot of news about six or seven goalkeepers that we want to buy but it is not true," Pellegrini said.
"There is no chance that Joe Hart could go out of this squad in January."
While Hart will make his return to action, having been dropped in recent weeks in favour of Costel Pantilimon, Pellegrini will be without injured captain Vincent Kompany (thigh) as well as Stevan Jovetic (calf), David Silva (calf) and Jack Rodwell (hamstring).
"Vincent began working with the squad this week. I think next week he will be fit to play, but he won’t be involved tomorrow night," the Chilean added.
"Jovetic, Silva and Rodwell will be out for one week or 10 days more, so they will miss tomorrow and Sunday (against Swansea City)."
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