The defender is also wanted by Paris Saint-Germain and Manchester United, while Everton boss Carlo Ancelotti wants to be reunited with him at Goodison Park.
Koulibaly is also a Newcastle United target, with the new owners willing to offer him €12million-a-year, but he is keen to move a club offering Champions League football, with the Reds clear favourites.
The Senegal international is expected to leave Napoli this summer, and the Serie A giants have slapped £100 million on his head.
However, the coronavirus pandemic could see them agree to a much lesser fee, and it will be interesting to see if Liverpool will be able to meet their demands.
Klopp dreams of a Virgil van Dijk-Kalidou Koulibaly centre-back partnership, and that will unarguably be the best in Europe.
The 28-year-old is one of the best centre-backs on the planet, and having him in the Liverpool backline will further make the side hard to beat.
Liverpool are six points away from winning the Premier League and will look to strongly challenge across all competitions next term having been dumped out of the Champions League by Atletico Madrid.