The Pachuca forward, who scored three goals at the 2014 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.
Goal understands talks with the Mexican club are already at an advanced stage and a source close to the deal has revealed that the Hammers are keen to learn of Valencia's intentions by Wednesday of this week, "one way or another."
Aaron Cresswell, Cheikhou Kouyate, Diego Poyet and Mauro Zarate have already 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 £12 million 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.
And the former Bolton boss confirmed that the deal was nearing completion, stating: “We’re very close, but nothing is ever certain in this game with new signings until they have actually signed on the dotted line.
“We are very hopeful, there has been a lot of negotiation done by the chairman and hopefully that will pay off in the next 72 hours.”
Allardyce has also targeted Dnipro's Yehven Konoplyanka, and the club are believed to retain an interest in the winger despite having an initial £9.5m bid turned down last week.