Slaven Bilic has confirmed West Ham’s interest in Tore, but they have been unable to do a deal so far.
The Hammers have apparently made a loan bid with a view to making the deal permanent next season, but Besiktas have rejected the offer.
“We received a loan offer with a buyout clause option which we rejected,” Orman confirmed.
Whether West Ham will make a repeat offer for Tore remains to be seen.
Besiktas initially seemed determined to keep hold of the wide-man, but their stance has relented slightly in recent weeks.
Following Tore’s admission that he would like to move to West Ham, Orman has suggested that a deal could be possible in the fuutre.
“We have not transfer listed Gokhan Tore he is a very important player but if he wants to leave we will sell him for the right price,” he added.
West Ham are expected to invest heavily in their first-team this summer, with Slaven Bilic set to be backed with funds.
The Hammers have already made two signings since the season finished, after completing deals for Håvard Nordtveit and Sofiane Feghouli.