Fellaini's current deal with the 20-time English champions will expire at the end of next month.
The Belgium international had been widely tipped to leave United this summer, but after scoring the winner against Arsenal in the Premier League on Sunday afternoon, Red Devils boss Jose Mourinho hinted that the midfielder would be staying at the club.
Fellaini has also revealed that he would be open to a move to the Chinese Super League, although it is thought that the 30-year-old's first choice is to sign a new deal at United.
"The entire staff is doing everything I can to stay. Now I am in a strong position, especially since Mourinho has stated that he wants to keep me," Fellaini told Sport.
"Last year I went to the coach and I said that I wanted a new contract. I then had a second meeting, but I will not ask it ten times. Afterwards I became important for the team... and a good player costs at least €50m (£44m). The club knows that they went wrong there.
"I would not have a problem with life in China. I love to discover other places and other cultures. And I will not go there alone. If I go, it's with the family. I am now thirty years old, end of contract and negotiating with Manchester United. There are several clubs that show interest. I'm waiting for what's going to happen."
Fellaini has scored five times and 22 appearances for United during the 2017-18 campaign.