The 25-year-old, who scored three goals at the World Cup, currently plays for Mexican side Pachuca.
The forward has also attracted interest from Sevilla and AC Milan this summer.
However, the Hammers will take the forward to Upton Park for a fee of £12m, according to talkSPORT.
It is believed that Valencia will sign a five-year deal with the Premier League outfit.
Valencia has scored 18 goals in 23 appearances for Pachuca since joining them in January.