0259 GMT January 23, 2020
Former England international Lampard, who was released by Chelsea at the end of last season, has made a strong impact after joining the champion on a short-term move from sister club New York City, pasport.com reported.
That arrangement is due to expire at the end of December with the plan for the 36-year-old then to report to New York for pre-season training ahead of the new club's first Major League Soccer campaign.
But Lampard's form has raised the possibility of the loan being extended and, with fellow midfielder Yaya Toure set to play at the African Nations Cup from January, that would especially benefit City.
Pellegrini, from his point of view, wants Lampard to stay in Manchester but he is also aware of the bigger picture concerning City's bold project in the MLS and he also wants to respect the player's wishes.
That makes the decision less than straightforward and Pellegrini, despite being asked repeatedly, cannot yet confirm anything.
He said, "Before December finishes we will have a decision but, as I repeat, I think Frank is a very important player for us and I hope we will not have any problems for him to stay here.
"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."
Asked again at a press conference on Friday if he wanted Lampard to stay, Pellegrini said, "Of course. He's a very important player for us and we need him in this moment.
"He couldn't start in the US until January or February, so prefers to stay here until December. If he can finish the year here, better — but I think that the MLS is a very important league also and I think that Frank Lampard will be very happy in the United States."