The Hammers are keen to sign the Pachuca striker and have agreed terms with the Ecuadoran but are continuing to negotiate with the Mexican club over a fee for the 25-year-old.
The Hammers have targeted the Ecuador international as Sam Allardyce looks to bolster his forward line ahead of the 2014-15 season, and Valencia flew into London for talks with the east Londoners on Sunday.
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The Pachuca striker has subsequently agreed to become a West Ham player, with the club understood to have offered Valencia a five-year contract, although negotiations with the Mexican club over a fee for the player - who is rated at around 19 million euros - are continuing.
Pachuca's chairman Jesus Martinez has previously insisted that Valencia will not be allowed to leave the club for a fee under the Mexican league record, telling reporters: "I won’t talk about prices, but if he is sold, it will be the highest transfer fee ever in Mexican football, otherwise he won’t be sold."
Should the two sides agree a deal, a work permit will then have to be arranged but sources close to the deal insist West Ham foresees no problems with the process, given that Valencia ended the season as the top scorer in his domestic league.
Allardyce has already acquired four new players in the close season, with Aaron Cresswell, Cheikhou Kouyate, Diego Poyet and Mauro Zarate arriving at Upton Park, and the club is now pressing ahead with plans to sign Valencia.
The 25-year-old scored all three of his country's goals at the World Cup.