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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.