Het Nieuwsblad says the Hammers have offered €15m for Vanaken this week.
West Ham boss David Moyes is a fan of Vanaken, but Brugge management are reluctant to sell. Indeed, they're seeking over double to part with Vanaken before the market shuts.
The 28 year-old has a deal to 2024 with Club Brugge.
Vanaken has been likened to Tomas Soucek, who joined West Ham in January.
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