Fellaini has entered the final year of his current deal at Old Trafford.
An initial proposal has been tabled to the 29-year-old midfielder.
Jose Mourinho personally urged United chiefs to tie him down to fresh terms.
Fellaini is yet to start a game this season but inspired United to victory as a substitute in the Champions League against Basel on Tuesday.
Mourinho has publicly praised the big Belgian for what he brings to the team.
He explained: “I have always thought of Fellaini as a player with special qualities.
“You always want a player like that in your team or squad.”
United have a policy of only offering one-year deals to players over the age of 30.
Fellaini, who joined from Everton in 2013, reaches the milestone in November.
According to the Mirror, Fellaini is looking for a longer-term contract but is enjoying his spell under Mourinho’s management.