The report claims that the Hammers made a £9 million bid but that the Black Eagles want at least £13 million for their star man.
The East London based club initially made a loan offer with a buyout clause option according to Besiktas president Fikret Orman but the deal was rejected.
“We received a loan offer with a buyout clause option which we rejected,” Orman stated in his press-conference.
Besiktas are open to the prospect of Tore joining West Ham but will only accept a permanent transfer deal.
West Ham are reported to have already agreed personal terms with Tore who wants to make the move a source close to the club told Turkish-football.com.
Tore is keen on the prospect of working with Slaven Bilic again after establishing himself as one of the most sought after players in the league under his stewardship.
The explosive winger was a key player under the management of Bilic and maintained a close relationship with the Croatian manager following his Besiktas exit.