In January, Stoke paid £14m to sign N'Diaye from Galatasaray but despite contributing two goals from 13 appearances, the Potters were relegated from the Premier League.
A number of high-earning players are expected to depart the bet365 Stadium before the start of the next campaign, and it appears that the Senegal international will be among the names to look for a new club.
D'avilla told Radyospor: "Badou likes challenges. He has a right to leave Stoke City to play on a bigger platform like the Champions League. It's not cool for me to say specific things about his transfer at this stage but I can say things will become much more clear after the World Cup.
"I can confirm that he will leave Stoke City. There has been contract from Spain. Turkey is an option for us as well. He could go to Besiktas or Fenerbahce or any other club. It's all down to negotiations with Stoke City."
N'Diaye has four years remaining on his contract but it has been suggested that the player has a relegation release clause in his deal.