The Hammers have long been interested in the services of the 29-year-old, having made an offer of €15m to sign the midfielder in the summer of 2020.
Vanaken was the second-highest goalscorer in all competitions for the reigning Belgian champions during the 2021/22 season behind Charles De Ketelaere, who joined AC Milan this summer.
West Ham are set to rekindle their interest in the Belgium international this summer following the exit of Nikola Vlasic to Torino on loan with a purchase option.
Vanaken made 50 appearances in all competitions for Club Brugge last season, scoring 15 goals and laying on 12 assists.
So far this season, Vanaken has made four appearances in the Jupiler Pro League and scored a solitary goal.
The 29-year-old midfielder is under contract until the summer of 2025 and it could take a substantial offer to prise him from the Belgian champions.
It remains to be seen whether Vanaken moves to the London Stadium this summer after spending the past seven seasons in Bruges.
Club Brugge may be reluctant to lose their vice-captain so soon after De Ketelaere’s departure, given the transfer window closes in a little over two weeks.