The Pachuca striker, who scored three goals at the World Cup before his country's group stage elimination, has been targeted by Sam Allardyce as the Hammers boss continues to reshape his squad ahead of the 2014-15 season.
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Goal UK reports talks with the Mexican club are already at an advanced stage, and a source close to the deal says the Hammers would like to learn of Valencia's intentions "one way or another" by Wednesday.
Aaron Cresswell, Cheikhou Kouyate, Diego Poyet and Mauro Zarate already have arrived at Upton Park this summer and the club are now pressing ahead with plans to sign Valencia.
The 25-year-old is valued at around 15 million euro by Pachuca, having scored 23 goals in all competitions last season, and the East Londoners are understood to be prepared to match his asking price as Allardyce looks to deliver a top-10 finish in 2014-15.
Allardyce has also targeted Dnipro's Yehven Konoplyanka, and the club is believed to retain an interest in the winger despite having an initial €12m bid turned down last week.