New Everton boss Marco Silva has the backing of his football director Marcel Brands to try and pursuade West Hanm, who value the striker at £50 million.
This happens to be more than what the club paid Stoke city to have for Marko Arnautović last summer.
However, New Toffees are facing competition from Manchester United who remain favourites to land the 29-year-old this summer.
United are ready to cash in for some high earners before bringing in new recruits, which could open the door for other clubs to bid.
And Everton are set to go in early for the Austrian whose 11 Premier League goals saved West Ham from the drop last term.