Olivier Giroud's contract is running out at Chelsea, with the deal coming to an end once the season is over. Giroud signed for the 'Blues' from Arsenal in an 18-month deal last January.
Besiktas are in the market for a forward, after Alvaro Negredo left for Al-Nasr this summer and Cenk Tosun joined Everton in January.
According to 'Goal Turkey', Giroud has been identified as Besiktas' main target and will try to open negotiations with the 31-year-old in January.
The Frenchman is yet to score for Chelsea this season, and has struggled to get regular game-time under Maurizio Sarri.