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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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?