United are in the midst of their worst start to a campaign for 30 years ahead of their clash against table-topping Liverpool at Old Trafford on Sunday.
The club have come under fire for failing to replace Romelu Lukaku in the summer following his sale to Inter Milan.
United have been strongly linked with Juventus striker Mario Mandzukic but the Croatian now looks set to join AC Milan.
And, according to the Express United have now turned their attention to Dembele who has starred in Ligue 1 since his switch from Celtic in 2018.
He has hit 26 goals in 56 games in all competitions for Lyon and plundered 20 strikes in his debut term in the French top flight last season.
Lyon paid just under £20million and will be looking to make a healthy profit on the 23-year-old should they cash in during the winter window.
United have been left short up front after selling Lukaku and loaning Alexis Sanchez to Inter.
Ole Gunnar Solskjaer added only Daniel James, Aaron Wan-Bissaka and Lee Grant to his squad in the summer and, if results go against them, United could end this weekend in the Premier League relegation zone.