The Hammers are keen to bolster their midfield options and have identified the Kenyan international as a viable option, say Football Insider.
Wanyama, 27, moved to North London from Southampton two years ago for a bargain £11million.
He enjoyed a strong first season under Mauricio Pochettino, making 47 appearances.
But a serious knee injury interrupted last term and the big midfielder has struggled to regain his place in the starting line-up ahead of Eric Dier, Mousa Dembele and Harry Winks after his return to fitness.
Wanyama has featured five times for Spurs this season and one of his two starts was against Barcelona at Wembley in the Champions League defeat earlier this month.
West Ham have deployed central defender Declan Rice in central midfield this season, but want to add an experienced midfield enforcer to help push their climb up the table.
Meanwhile, Hammers boss Manuel Pellegrini has a fight on to keep hold of Issa Diop, whose impressive start to life in the Premier League has attracted interest from Paris Saint-Germain.
The moneybags French outfit are prepared to offer £50m for the centre-back who moved to the London Stadium for £22m from Toulouse in June.
Pellegrini’s side are back in action after Saturday's draw at Leicester against Spurs in the Carabao Cup on Wednesday night.
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