It is understood West Ham’s offer would include an option to buy, but Juventus would prefer to sell outright and value the Argentine at around £36m.
Higuain spent the end of last season on loan at Chelsea, scoring five times in 18 appearances for the west London club. But he has since returned to Italy, where he is now managed by Maurizio Sarri – the man who brought him to Stamford Bridge last season.
The Hammers are in the market for a striker after seeing forwards Marko Arnautovic, Andy Carroll and Lucas Perez all leave the London Stadium over the summer.
West Ham have not yet given up on trying to sign Maxi Gomez from Celta Vigo, even though the prospective deal appeared to be off because the two clubs could not agree on a payment structure for the player’s £45m release clause.
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