Genk, Eintracht Frankfurt, Feyenoord and PSV Eindhoven are also reportedly in the chase.
Ugbo was on loan at Cercle Brugge last season, scoring 17 goals across all competitions.
The 22-year-old is currently in the final year of his contract, and the Blues will have to cash in this summer or lose him on a free transfer next year.
West Ham’s interest in the highly talented forward certainly makes sense as David Moyes needs to add more depth to his attacking options.
The Hammers were reliant on Michail Antonio for goals this past season but require a more natural goalscorer, and Ugbo could be a solid long-term investment.
The youngster has the potential to develop into a quality Premier League player with coaching and experience.
Ugbo would cost around €3-5 million, and the transfer could represent an excellent bargain for the Hammers.
He will be hoping to join a club where he can play regular first-team football to further his development.
Whether West Ham or Fulham will pay the asking price is unclear, but there is no doubt that Ugbo would be a low-risk signing for the fee quoted.