The Hammers are locked in negotiations with Besiktas and want to secure a lower transfer fee. Talks are ongoing and a deal is expected to be reached at some stage this week unless a fee both sides are willing to accept is not agreed upon.
The Sun meanwhile reported that it is already a done deal and that Tore will wear the number 7 shirt for the East London based club next season.
Tore currently also wear the number 7 shirt for Turkish Super League champions Besiktas.
The explosive winger excelled under Slaven Bilic during his time in charge of the Istanbul giants and the Hammers boss has made no secret that he wants to be united with Tore.
Bilic recently revealed that he tried to sign Tore at the start of the season in an interview with the Socrates magazine.
“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 said.
“I tried to sign him at the start of the season but it was not the right time.”