The Black Eagles who signed Demba Ba from Chelsea last season are now plotting a second rain on Chelsea for their French international.
Besiktas are on the hunt for a new striker after selling Demba Ba to the Chinese club Shanghai Shenhua for €13 million.
Remy has found himself on the fridges of the squad after being signed from QPR last summer.
The 28-year-old provided two assists and scored nine goals in 29 appearances for the Blues in all competitions.
Remy has previously played for QPR, Newcastle United, Marseille, Nice, Lyon and Lens.
The French international who has three years remaining on his contract is expected to be available for around €14 million.
Beşiktaş finished the Turkish Super Lig season in third place and will play in the Europa League next season.