The Red Devils have been in the market for a new centre-forward since letting Romelu Lukaku leave the club last summer and were linked with a whole host of options during the January transfer window.
Odion Ighalo was eventually brought in on loan and remains an option to sign permanently, but Dembele, who has 22 goals for Lyon this season, appears to now be their number one choice.
Here, Sports Mole looks at which shirt numbers would be available to the 23-year-old should he arrive at Old Trafford.
Dembele wears the number nine shirt at Lyon and, given his position, would presumably be keen to take that number at Manchester United too.
The likes of Sir Bobby Charlton and Andy Cole have adorned that jersey before, but it is currently in the possession of Anthony Martial and would therefore only be available in the unlikely event that the Frenchman is sold or chooses to give it up.
It is a similar story for the number 10 shirt Dembele wore during his prolific time at Celtic, with Marcus Rashford the immoveable incumbent there.
The Frenchman may therefore have to go back to his Fulham days, where he wore the '25' when he broke into the first team.
As things stand that number is also taken by Odion Ighalo, but any deal for Dembele is likely to end United's interest in their current loanee and so that shirt number should become available.
If Dembele opts for a new number then the iconic '7', previously worn by the likes of George Best, Bryan Robson, Eric Cantona, David Beckham and Cristiano Ronaldo, will be an alluring option, but reports suggest that fellow target Jadon Sancho has already been offered that number.
The currently-unclaimed '11' is therefore a more realistic option, and that would see Dembele follow in the footsteps of United's all-time record appearance-maker Ryan Giggs.