Hart has been back to his best this season and the club have been in negotiations over a new deal.
The 27-year-old's current contract expires in the summer of 2016.
Pellegrini said: "I think it's an issue that we're talking about. Joe knows what I think about that. I think in the right moment, (we will) have the right solution. I think Joe wants to stay here and we want him to stay."
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