Spurs signed the French international for £30m following his impressive showing at Euro 2016 where Portugal defeated France 1-0 after extra time in the final.
But the former Toulouse and Newcastle United winger has struggled for game time in north London and may well be free to move on during the current transfer window.
While Trabzonspor are keen on a loan spell, Mauricio Pochettino’s charges are reportedly keen on an outright sale.
Vice-chairman Gencaga Meric told Turkish-Futbol: “Sissoko is keen on joining, we have spoken with him and talks went well.
“We have yet to convince Tottenham or their manager. Tottenham want to recoup most of what they invested in Sissoko but we want him on loan.
“We have made our offer and are waiting for a decision.”
Sissoko played just eight times in the Premier League last season but impressed as Spurs defeated Juventus 2-0 in a friendly at Wembley on Saturday.