Talks are reportedly ongoing between the club and Belgium international's representatives but it is understood that United's latest offer falls short of what Fellaini's camp are holding out for.
United boss Jose Mourinho is a big fan of Fellaini, who started his first game of the season against former club Everton on Sunday.
However, he is in the final year of his contract at Old Trafford and turns 30 in November.
United's policy has generally been to offer one year rolling contracts to players over 30 but Fellaini ideally wants a longer deal.
He has already been eyed up by clubs from Italy and Turkey and the 29-year-old will be free to talk to foreign clubs from January ahead of a potential free transfer in the summer.