The Manchester Evening News says Dembele would find it hard to turn down a move to United this summer.
Ole Gunnar Solskjaer is looking to add some attacking firepower in the next transfer window and the Lyon striker has been on the club's radar for some time.
And sources close to the player believe he would be impressed by the prospect of moving to Old Trafford.
But they also say United have not yet made contact with the French side.
Dembele is almost certain to leave Lyon who finished seventh in Ligue 1 after officials agreed to cancel the season due to coronavirus.
This means they will miss out on the Champions League next season while United still have a chance of making the competition if the Premier League campaign is completed.
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