The Daily Mail says Fellaini has still to accept United's offer of a new contract.
Talks are ongoing between the Belgium international's advisers and the club.
But United's latest proposal is understood to have fallen short of what Fellaini's camp wanted.
He is in the final year of his contract and turns 30 in November.
United's policy has been to offer one year rolling contracts to players over 30 and Fellaini would ideally want a longer deal.