It's claimed that the Spaniard can leave the Stadio San Paolo this summer if his €6M release clause is yet.
The big challenge though which the incoming Chelsea manager would face is to convince the board to sign the Belgium striker as he is already 31-years old and would cost a fortune in the transfer market. He has proven himself able to still compete at the top level.
But Napoli are adamant that they are due compensation if Chelsea name Sarri as their new tactician because he is under contract until 2020, with the manager's lawyers said to be arguing otherwise.
"[Chelsea fans] can expect nice football because he is a very good coach", Koulibaly told talkSPORT after Senegal's win. Sarri is a disruptive, savvy coach that can reinvigorate Chelsea.
There have also been reports that several senior players are unhappy with his demanding training regime.
Golovin has been with CSKA his entire professional career after progressing through their youth ranks and has developed in to one of the best players in Russian football since breaking in to the first team set-up three years ago.
But a number of reports have linked the 30-year-old with a move away from Turin this summer.
The centre-half was the subject of a summer-long pursuit by Chelsea in 2016, and was again wanted 12 months ago, but he has suggested he will be staying at Napoli to work with Sarri's successor Ancelotti.