The 17-year-old has been earning rave reviews for his performances for the Londoners’ youth sides, alerting a number of clubs from across the country.
Liverpool and United are thought to be leading the queue for the striker.
Scouts from the Reds travelled to watch the teenager net twice for the Cottagers’ U-21 side in the week, while their bitter rivals have been monitoring his progress.
Dembele only arrived at Craven Cottage from Paris Saint-Germain last year, but has been making a huge impact with his all action displays.
The Frenchman is a robust, yet skilful, player, and has been tipped to for a bright future.
Despite having a number of talented young attacking players, Brendan Rodgers feels that Dembele can add something different to his options at Liverpool.
Meanwhile, United also see his talent and are keen to tie up a deal.
Fulham chief Martin Jol has already turned down offers for the starlet from Championship sides, due to his desire to keep him at the club.
Would Moussa Dembele be better off staying at Fulham?
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