The French stopper had been heavily linked with a January exit, with Norwich and Cardiff City reportedly showing interest.
He ultimately remained at Stadio Olimpico, but it appears he could still be leaving the Biancocelesti this winter.
According to Il Corriere dello Sport, Besiktas are set to make an official approach to sign the experienced defender.
And with Lazio chairman Claudio Lotito not interested in loan deals, it is clear the Black Eagles will have to splash the cash if they want to sign the player before tomorrow’s deadline.
Mickael Ciani joined the Biancocelesti from Bordeaux in the summer of 2012, and went on to make 31 Serie A appearances for the club.
He never quite managed to nail down a regular starting berth and could now be leaving the Stadio Olimpico outfit in search of first team football.