Vincent Kompany could leave Manchester City this summer
Club officials are said to be drawing up a contract for the Belgium international and hope a deal can be done within a week.
That is according to Turkish newspaper Fanatik, who claim a Besiktas president Fikret Orman is monitoring the situation.
According to the report, meetings have taken place at board level.
Vincent Kompany - Spotlight on
The centre-back limped off in the second leg of City's Champions League semi-final defeat at Real Madrid in May and was subsequently forced to miss Euro 2016.
City are also said to be in talks with Besiktas' rivals Galatasaray over a £3m loan deal for Wilfried Bony, with a £17m clause inserted in the club want to make the move permanent.
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy