Upton Park side chase Goodison Park wide-man.
Upton Park boss Slaven Bilic saw Stewart Downing leave for Middlesbrough over the summer and has earmarked a move to bring in 27-year-old Mirallas as a replacement for the English winger.
Belgian international Kevin Mirallas has proven a very effective performer over the course of his three seasons at Goodison Park, netting 28 goals in 106 appearances, and Everton already turned down an initial £6m bid from the East London side.
West Ham target Everton & Tottenham attackers as Slaven Bilic looks to replace Stewart Downing
West Ham consider ambitious move to sign Man United star
Man Utd eye West Ham man as Van Persie replacement, striker transfer to happen this week
Bilic has already secured deals to sign Pedro Obiang, Angelo Ogbonna and Dimitri Payet thus far this summer and the Croatian has brought in Carl Jenkinson and Manuel Lanzini on season long loan spells.