Hammers boss Slaven Bilic knows Tore well from his spell in charge of Besiktas and had been hoping to take him to Upton Park in the current transfer window.
The English side even slapped in a €10m proposal for Tore, but all the signs are that Besiktas do not want to sell.
West Ham sent a representative to Turkey to speak to Besiktas president Fikret Orman and a promise was made to talk again about the player at the end of the season.
The 23-year-old joined Besiktas, initially on loan, from Russian side Rubin Kazan in 2013.
