The 22-year-old scored 25 league goals and assisted eight others in 43 games for the Championship side last term, and is attracting a lot of suitors from the Premier League.
Aston Villa, Sheffield United and Brighton and Hove Albion are all keen on Maupay, while he is also on the radar of clubs in Spain.
West Ham need a quality striker next season as manager Manuel Pellegrini looks to lead them to Europe, and have identified a couple of targets as they look to secure a replacement for Marko Arnautovic.
The Hammers are ready to lure the former St Etienne man to the London Stadium with a massive increase on his current wages and will offer him a five-year deal.
They have been told they have to bid in excess of £15million to have a chance to land Maupay, though, and it could end up being a bargain fee should he hit the ground running in the top-flight if signed.
The Bees’ star also scored three goals in four F.A Cup appearances last term, and given that he already knows all about English football, West Ham shouldn’t hesitate to take a punt on him ahead of other targets.