Fellaini, who only started his first Premier League game of the season in the 4-0 win over Everton on Sunday at Old Trafford, is into the final year of his contract.
The afro-haired Belgian turns 30 in November and United have a tradition of not handing long-term deals to players when they reach that milestone.
Fellaini was close to joining Galatasaray over the summer before Jose Mourinho pulled the plug on a deal.
And as far as the midfielder’s future is concerned, the Daily Mail claim United’s latest contract offer is deemed unacceptable to the player’s camp.
The report suggests talks are ongoing, although it is unclear when there may be a breakthrough in negotiations.
The Mail also claim that Fellaini would prefer to receive a longer extension too.
Mourinho was full of praise for Fellaini last week, insisting he feels ‘weaker’ without him in his squad.
“I have always thought of Fellaini as a player with special qualities,” Mourinho said.
“You always want a player like that in your team or squad.”
United face Burton in the third round of the Carabao Cup tomorrow (8pm).