United triggered a one-year extension in the 30-year-old's contract at the start of the year, but agreeing a deal beyond the end of the current campaign is proving difficult.
"They made a proposal, probably another will follow. Whether I will accept it, I do not know.
"We will see. You cannot arrange something like that in a jiffy," Fellaini told Belgian website HUMO.
"If Manchester did not want me anymore, they would have said that for a long time."
Fellaini can begin talks with clubs when the January transfer window opens on Monday and could leave for nothing when his current contract expires at the end of the season.
The Belgium international has discussed his situation with Mourinho but does not expect it to affect his relationship with the manager.
"We talked about it. The coach is someone who respects the decisions of his players," he said.
Fellaini, who has played nine league games and scored three goals this season, is currently sidelined with a knee injury.