Reports on Tuesday suggested that Hart could be loaned to Stoke City, with Pellegrini hoping to use the England international as a make weight to sign Asmir Begovic.
Hart has already been confirmed as a starter for Wednesday night's Champions League game against Viktoria Plzen and Pellegrini ruled out the suggestion that the goalkeeper is 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," he said. "There is no chance that Joe Hart could go out of this squad in January."
While Hart will make his return to action on Wednesday, having been dropped in recent weeks in favor 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).
City, which sits second in Group D behind Bayern Munich, has already qualified for the last 16 of the Champions League.