Hart has been linked with a loan move to Stoke, as part of a deal that would see Asmir Begovic move to Eastlands.
But Pellegrini insists the England international keeper will not be leaving.
“There is a lot of news about six or seven goalkeepers that we want to buy but it is not true,” said the Chilean.
“There is no chance that Joe Hart could go out of this squad in January.”
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