Lampard, who joined New York after being released by Chelsea at the end of last season, is on loan at City until the end of the year and has scored three goals in 10 league appearances.
The 36-year-old is due to return to America for pre-season training in January ahead of the start of the MLS season in March.
City manager Pellegrini now hopes the two clubs, who are both owned by the Abu Dhabi-controlled City Football Group, can agree a deal to keep Lampard in Manchester.
"I think Frank is a very important player for us and I hope we will not have any problems for him to stay here," Pellegrini, whose team are second in the league and three points adrift of leaders Chelsea, told reporters ahead of City's visit to bottom-club Leicester City on Saturday.
"But I cannot say just from one side what will happen with him. He has a loan just until the end of December and there is another club involved.
"The MLS is involved also. There are a lot of parties with an arrangement. It's not just depending on one opinion. But I hope we can have a decision as soon as possible because it's important for us and the players."
Lampard has enjoyed a number of impressive displays during his short time at the Etihad Stadium and is seen as important cover for Ivorian midfielder Yaya Toure, who will be unavailable during January should he play at the African Cup of Nations.
Media reports said the English champions and New York are due to meet this week to decide Lampard's immediate future. MLS commissioner Don Garber said this month that the American league would not get involved in the decision.
(Reporting by Sam Holden, editing by Ed Osmond)
Share
