Fellaini's current deal is set to expire at the end of the season and if United can not reach another agreement before January 1, the 29-year-old will be free to sign a pre-contract with another club.
"We gave Michael Carrick a contract because we think he's a good player and an important player".
United signed Nemanja Matic from Chelsea for £40m this summer.
And Fellaini has made a perhaps unexpected splash at Old Trafford this season; the Belgian has claimed goals against Leicester City and FC Basel and produced a commanding display on his first start of the season against Everton.
"He is just in a team where at this moment Matic and Fellaini are in the best form that I have ever seen them in".
"That's a team, that's a squad, we can only play with 11 guys". I never saw Fellaini playing so well.
"The United boss said: "(Sergio) Romero played the Europa League final, which was the game of the season for us and he is not playing. "You know, that's life at big clubs", he said.
"He gave us the stability that we were losing a little bit and then was only possible, in my view, 1-0 or 2-0, I never thought in the last 15 or 20 minutes it could be 1-1".
The Spaniard was once again overlooked for today's game against the Toffees as Marouane Fellaini was chosen to replace the injured Paul Pogba, but he did make an appearance off the bench and Mourinho talked up the midfielder's importance to his side's performance. For Carrick and for Ander it is just patience because their time will arrive. They are going to be important players for us, for sure. But we don't think we are far from Real Madrid - we won three titles last season, the only English team to do it.
"We need to have a strong team".
"Oh yes, serious because it's football, it's competition and we take it seriously", added the United boss.