Dembele has gone from strength to strength since joining Lyon from Celtic in a £19.7million switch last summer.
His goalscoring prowess is undoubted and he has 18 goals in all competitions so far this term.
United may look to beef up their attacking options and Romelu Lukaku's future could be uncertain.
Some reports have claimed Inter Milan striker Mauro Icardi, who has been on United's radar before, could leave the Serie A outfit for £52million in the summer.
As far as Dembele is concerned, United have already sent scouts to watch him in action and he has impressed according to .
Similarly, the Mirror suggest Arsenal are also mulling over a potential move and could swoop for the highly-rated 22-year-old.
Originally, it was thought that Unai Emery may be given just a £40m budget to play with in the summer, although that was if the Gunners don't finish in the top four.
With Danny Welbeck out of contract in the summer, Emery supposedly wants to bring a proven forward to provide competition for Alexandre Lacazette and Pierre-Emerick Aubameyang.
The Mirror claim that Emery has also identified Bournemouth's Ryan Fraser as a potential option.
Lyon, the Mirror suggest are aware of interest from Premier League clubs.
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Dembele is a sharp shooter and while he has relatively little experience playing in England's top flight, his pace and power makes him an enticing proposal.
Although United can already call upon Lukaku, Rashford and Anthony Martial, a deal for Dembele would make their rivals sit up and take notice.