The former England international agreed a switch to New York City - an affiliate club of the Premier League champions - in July, but has been at the Etihad Stadium since with the next MLS campaign not beginning until March next year.
Though expected to remain in England until December, Lampard has shown his top-flight qualities remain with six goals in 14 appearances - only Sergio Aguero has more for City this term.
Lampard's winning goal in Saturday's 1-0 win at Leicester City was his 175th in the Premier League, drawing him level with Arsenal legend Thierry Henry.
While Pellegrini has been clear about his desire to keep the former Chelsea man in Manchester beyond the New Year, the Chilean now believes Lampard wants the same.
“We know exactly what we must do," Pellegrini said.
"Frank wants to stay, we want to keep him. Now we must resolve the problem with New York City and the MLS."
Edin Dzeko picked up a calf injury in the warm-up at the King Power Stadium, and Pellegrini revealed after the win he expects to be without his three senior strikers - the Bosnian, Aguero and Stevan Jovetic - for the remainder of the festive period.
Pellegrini hinted afterwards he would delve into the transfer market in January to ease the burden on his front men, but dismissed any notion that his lack of options up front was a driving force behind the pursuit of Lampard's longer-term signature.
He added: "The decision about Frank can have nothing to do with the injuries. Dzeko could be fit and Aguero and it would be the decision of Lampard.
"He will not stay with us because we have injured strikers. He'll stay with us because he us a very important player."
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