The South American forward was in excellent form for his nation in Brazil, netting three goals in three games as they narrowly missed out on qualification for the last 16.
Although the tournament ended in disappointment for the 25-year-old, his reputation has been boosted, which has attracted the Hammers.
Mexican club Pachuca are said to be ready to cash in on Valencia, with £10m offers likely to be enough to get him across the Atlantic Ocean to Europe.
Irons representatives are understood to be working on a deal – which may be complex – but there is a feeling of confidence in east London.
Valencia netted 18 goals last term, and is seen as a good option by Allardyce as he plots to bring a more attractive playing style to Upton Park after criticism last season.
West Ham have already snapped up Mauro Zarate, Aaron Cresswell, Diego Poyet and Cheikhou Kouyate this summer, and have tabled an offer for Yevhen Konoplyanka.