The 27-year-old joined the Hammers from Pachuca, another club in Mexico, for £12.5m in 2014 after impressing for Ecuador at the World Cup in Brazil.
However, the forward struggled for consistency at the East London club and managed to score only 10 goals in 66 appearances before being sent out on loan to Everton last season.
Valencia scored only three goals in 23 appearances for the Toffees, prompting them not to activate the option to make his move to Goodison Park permanent.
According to Sky Sports News, the Hammers are keen to offload Valencia this summer and remain hopeful that a deal can be struck for the right price.
West Ham finished 11th in the Premier League table last season.