That's according to French news outlet Le 10 Sport who say Monaco view Dembele as a potential replacement for Kylian Mbappe.
The Ligue 1 champions will face stiff competition from the Hammers, though.
It's suggested the Premier League outfit are serious suitors and Slaven Bilic has already made an offer.
Dembele is on the radar of a host of Europe’s top clubs.
Chelsea and Arsenal have both been sniffing around after the 21-year-old’s impressive displays north of the border.
But Le 10 Sport say West Ham now looks the most likely Premier League destination.
Dembele bagged 32 goals in 48 games after signing from Fulham 12 months ago.
But despite significant transfer speculation surrounding his prized asset, Celtic boss Brendan Rodgers has previously stated he's calm about the situation.
Speaking earlier this summer, he said: "I counted the other day, Moussa has been linked with 10 clubs.
“It was Marseille the other day, I saw Arsenal the other week, there was Paris Saint-Germain, there was Chelsea so there is nothing in it from our perspective.
"I felt if he progressed the way we thought he'd progress and if he wanted to move any time it would be after the second year.
"There is no rush from Moussa's perspective.
“He is a player that we really want to keep and if anything (offer) did come in we would assess it."
