The Baggies yesterday agreed a fee believed to be worth around £12m plus add-ons for the West Ham winger.
And Diangana, who spent a successful loan spell with West Brom last season, will now be allowed to talk terms with Slaven Bilic’s side.
But Fulham are also interested in the 22-year-old, who is under contract with the Hammers until 2025.
Boss Scott Parker kept a close eye on Diangana last season and would like to bring him to Craven Cottage.
While talks are at an advanced stage with West Brom, it is understood a deal is far from done, with the player’s representatives waiting to see if other clubs come in.
Aston Villa also expressed an interest in Diangana, but Fulham are more likely to launch a last-minute bid.
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West Ham do not want to sell the England Under 21 forward, who manager David Moyes wants to integrate into his first-team squad this season.
But the Hammers need to sell to buy this summer and are struggling to offload higher earners like Jack Wilshere, Felipe Anderson, Pablo Fornals and Manuel Lanzini.
Diangana also plays in a position where West Ham have plenty of competition - with Moyes keen to strengthen in other areas, primarily at the back.