The 17-year-old forward produced a scintillating showing for Fulham Under-21 side against the Red Devils, leaving United staff Steve Round, Phil Neville and Nicky Butt impressed in the process.
As a result, United will attempt to lure the youngster to Old Trafford at the earliest opportunity, although that will be no easy task.
Dembele has just signed a professional contract at Craven Cottage, meaning a transfer fee needs to be negotiated with Fulham.
The Frenchman joined the Cottagers from Paris Saint-Germain last year for a nominal fee, and has since impressed playing for club’s youth sides.
With Fulham slowly becoming one of the main candidates for the drop, currently 9/4 to get relegated, chances are that Dembele would jump at the opportunity to leave the Cottagers for Manchester United in the January window.