His agent Jan de Visser claims United are now weighing up a fresh approach for the 25-year-old, who is also attracting interest from Real Madrid. Tottenham and Inter Milan.
Dembele has been a big hit at Craven Cottage since joining the west Londoners from AZ Alkmaar in 2010 for £5m, but speculation about his future is intensifying as he is entering the final year of his contract.
De Visser, of management agency Sport International, confirmed United's admiration in the player after news broke of Real's offer for his services which has also been knocked back by Fulham.
He told Dutch newspaper De Telegraaf: "They are not the first big club who have contacted us this summer for him."