Turkish journalist Baris Ozturk reported that Besiktas has submitted an official offer to PAOK for the acquisition of Kiril Despodov. The same information indicates that despite the interest from Besiktas, Despodov does not prioritize a move to the Turkish league. It is reported that the player is considering a move to a major league, with Serie A being his main target if he leaves PAOK. Besiktas considers that Despodov could immediately strengthen their attack due to his speed and experience, but the player's stance makes negotiations more difficult. Despodov's contract with PAOK is valid until the summer of 2027.

Kiril Despodov's agent recently conveyed a proposal from Beşiktaş, but the 29-year-old Bulgarian winger was not enthusiastic about the prospect of moving to Turkey. Despodov is aware that his performances for PAOK have kept him visible in the European market, and if he were to leave, his preferred next move would be to Italy. He feels he has a good reputation in the country and that his playing style is suited to Serie A. Although a transfer to Turkey is not his current priority, it is not ruled out for the future. The Bulgarian international, who has 60 caps and 15 goals for his country, joined PAOK in September 2023 and is under contract until June 2027. In the current Super League 1 season, he has scored two goals in 12 appearances. His market value is estimated by Transfermarkt to be €6.00m.