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, Mourinho hinted that the midfielder would be staying at the club.
Earlier this week, the 30-year-old said that he was in "a strong position" when it came to negotiating his future, and Mourinho believes that the midfielder will ultimately sign an extension with the Red Devils.
"I'm still positive. He's important, he's a player that I like but again, especially for him, he has a different position in relation to other players with contract because we can control other players' destiny in another way, in Marouane's case the destiny is in his hands," Mourinho told reporters.
"He knows I want him to stay, the club wants him to stay, he has an offer from us and it's up to him yes or no I am still positive as I feel he likes to be here, he likes the feeling of the manager trusting him and I think there is a good chance for him to stay but if he leaves so be it."
Fellaini has scored five times and 22 appearances for United during the 2017-18 campaign.