Valencia will cost West Ham close to the club-record $25m they paid Liverpool for striker Andy Carroll.
The 25-year-old scored all three of Ecuador's World Cup goals in Brazil this summer, attracting the attention of a number of Premier League suitors in the process.
But Hammers boss Sam Allardyce looks set to have won the race to sign him, and provided he passes his medical and agrees personal terms, the striker will leave his Mexican club Pachuca for East London.
He will become West Ham's fifth signing of the summer, joining Argentine striker Mauro Zarate, centre-back or midfielder Cheikhou Kouyate, Ipswich Town left-back Aaron Cresswell and Charlton midfielder Diego Poyet at the club.
Pachuca chairman Jesus Martinez said last week that he wants any deal to include clauses that would see Pachuca benefit if Valencia was to move on.
"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," he told Ecuagol.
"I won't talk about prices, but if he is sold, it will be the highest transfer fee ever in Mexican football football, otherwise he won't be sold.
"We are seeking the possibility that is convenient for him and the club and that he is sold for the price that we like. We want to keep a percentage of the player in case he is sold in the future to another big team in Europe.
"It hurts me, I don't want to sell him and neither does the manager or the fans but we can't go against the career the kid aspires to."