The former England international is currently on loan from MLS side New York City, who get their maiden campaign under way next season.
With New York not due to play in MLS until March and Lampard impressing for City so far this term, there have been suggestions the English champions will look to extend the 36-year-old's stay at the club.
Lampard - due to return to his parent club in January - has spoken of the possibility of extending his stay at the Etihad Stadium and Pellegrini confirmed a decision will likely be made in December.
"We are going to talk to all the parties and make a decision in December," the Chilean told the British press.
"If all parties agree then maybe we can keep him, but it could be that we want to keep him and Frank wants to go.
"I speak to Frank every day and I have the impression that he is playing better every day.
"I am certainly very happy with the loan so far."
