The Blues have already secured Liam Delap from Ipswich Town and are closing in on deals for Brighton’s Joao Pedro and Borussia Dortmund’s Jamie Bynoe-Gittens.
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Earlier this month, West Ham received a £50 million ($68m) offer for the Ghana international from Spurs.
According to the Daily Mail, the Stamford Bridge giants must offload players before making a move for Kudus, who is available this summer as the Hammers seek funds for their own transfers.
The 24-year-old has an £85 million ($116m) release clause for Premier League clubs, though the Hammers are open to offers and unlikely to demand the full amount upfront.