The report claims that a deal has been reached and that the Hammers will announce the transfer in May.
Besiktas are yet to release a statement regarding the claim but it is worth noting that Slaven Bilic started talks with West Ham around the same time last year despite reports at the time being denied by the club.
The Hammers have been keeping close tabs on Tore and Bilic confirmed that an offer was made for the Turkish international over the summer transfer window.
Tore does of course have Premier League experience having developed as a Chelsea youth before his move to Bundesliga side HSV.
After a brief spell at Rubin Kazan in Russia Tore joined Besiktas where he became one of the most highly sought after player in the league under the stewardship of Bilic.
The former Besiktas manager has made no secret that he is fond of the explosive winger and that he would like to see him at West Ham.
“Gökhan is a legend he is a top guy and a great player of course I would love to have him in the team,” Bilic told the Socrates magazine.
“I tried to sign him at the start of the season but it was not the right time.”