The Togo international was largely unimpressive for Spurs last season despite a late flurry of goals after joining Tottenham on a permanent deal from Manchester City in August.
André Villas-Boas has been linked with a host of striker already this summer as the Tottenham manager looks to bolster his attacking options at the north London club.
And Besiktas chief Piper admitted Adebayor would be a “dream” signing for the Turkish club but hinted any deal for the African would be protracted.
“It is certainly true that we are looking at the idea of a transfer. We have made a serious bid for Adebayor,” Piper told Fanatik.
“That, in turn, has given us a figure for the player, which is slightly above the amount that we imagined.
“However, making a signing as big as this immediately is nothing but a dream.
“Negotiations always take a long time. I hope that we will get a chance to have a meeting soon.”
Adebayor scored five goals in 18 Premier League starts for Tottenham last season.
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