Tosun left Besiktas to join Everton in January 2018, but returned to Vodafone Park in the last winter transfer window on a six-month loan spell.
However, the striker only made four appearances across all competitors for the Turkish against as his season ended early owing to a serious knee injury.
Besiktas are keen to have Tosun back in their ranks and club president Cerbi has revealed he has given him his word that he can play for them whenever he wants.
Cerbi revealed that if his club try to make two signings in the upcoming winter transfer window, the Everton man will be one of them, but stressed they are not against the idea of waiting for his services until May, when he will available on a free transfer.
“With regards to Cenk Tosun, you have my word”, Cerbi was quoted as saying by Turkish broadcaster Aspor.
“He is a football player who made money for our club.
“He suffered an unfortunate injury.
“I hope he returns well and very soon.
“We have promised him, he can [play for us] whenever he wants.
“For Kaan Ayhan, we will [make moves] when January comes.
“If we do make two transfers [in January], those will be Cenk and Kaan.
“[A move for] Cenk Tosun may also be in May. His contract is expiring [next summer].”
It remains to be seen whether Tosun will leave Everton for Besiktas in January or wait until next summer to join on a free transfer.