With Chelsea also keen, Spurs have agreed a £55m fee with West Ham for the Ghana international, says BBC Sport.
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Spurs are now scheduling a medical for Kudus with an agreement in place.
West Ham rejected a £50m offer from Tottenham on the weekend, but have now accepted an improved bid.
Kudus is now set to move to Spurs for £30m less than the £85m buyout clause in his Irons deal which came into effect this month.