The 25-year-old scored 18 times in 23 games for Mexican side Pachuca last season before impressing for his country at the World Cup in Brazil with three goals, scoring twice against Honduras and once against Switzerland.
He also scored against England in the 2-2 friendly draw in Miami before the tournament.
Pachuca president Jesus Martinez revealed earlier that an English club were closing in on the signing of Valencia.
"There are various offers for Enner Valencia, the strongest and closest to what the player and us are demanding is from a club from England. We are making huge steps to finalise the negotiation," Martinez told Ecuagol.
"We are seeking the possibility that is convenient for him and the club and that he is sold for the price that we like for everything the Mexican league is worth.
"We want to keep a percentage of the player in case he is sold in the future to another big team in Europe."
West Ham are keen to avoid the problems of last season when they were often light on options up front, with Andy Carroll already joined at Upton Park by Argentine forward Mauro Zarate.