The Chilean has quashed reports linking the England international with a temporary switch to the Potters in January, insisting that the goalkeeper is staying put
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Hart has already been confirmed to start 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 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).
City, who sit second in Group D behind Bayern Munich, have already qualified for the last 16 of the Champions League.