Ole Gunnar Solskjaer is on the hunt for a new man in attack after making Romelu Lukaku available for sale.
Dembele, who played for Fulham and Celtic before joining Lyon last summer, has emerged as a target for Solskjaer.
According to EuroUnited, Manchester United are ready to firm up their interest in the 22-year-old.
It is claimed Old Trafford bosses fancy submitting an offer worth €45m (£38.9m) but they face competition from Premier League rivals Arsenal and Liverpool.
The Red Devils reportedly have the upper hand, however.
EuroUnited claim Dembele is a fan of United boss Solskjaer.
A tweet from the EuroUnited account read: “@ManUtd wants to make an offer of 45M€ for Moussa Dembele (@OL).
In other Man Utd news:
“Supervised on several occasions, the French forward striker really likes Ole Gunnar Solskjaer.
“@Arsenal and @LFC have also expressed interest.”
After scoring 51 goals in 94 appearances across two seasons for Celtic, Dembele sealed a £19.7m move to Lyon last summer.
The France Under-21 international has scored 19 goals in 44 appearances in his maiden campaign for the Ligue 1 outfit.
He is under contract until the summer of 2023.
Celtic reportedly inserted a five per cent sell-on clause as part of the deal that took Dembele to Lyon.
They will net nearly £2m if the Frenchman joins United for €45m (£38.9m).