Tore, a player with whom Slaven Bilic has previously said that he would love to bring to east London was the subject of interest from the Hammers last summer, although the club were unable to complete a deal.
And Turkish outlet Kralspor claimed at the weekend that West Ham had reignited their interest in the 23-year-old German -born goalscorer, who moved to Besiktas from Russian outfit Rubin Kazan on a permanent basis in 2014 after having spent the previous season on loan at the Vodafone Arena.