The Napoli ace, 31, is attracting plenty of attention as he moves into the final 12 months of his contract at the Serie A side.
A transfer fee of £35million is likely to finally prise him away from Italy, with Koulibaly also wanted by Juventus, but Napoli president Aurelio De Laurentiis is refusing to sell to them.
Meanwhile, transfer journalist Fabrizio Romano says the transfer will be announced in the coming days, with the 31-year-old set to sign a five-year deal which will see him pocket €10million (around £8.4m).
And the player seemed to admit as much when asked by French journalist Romain Collet-Gaudin. "I'll confirm that later, but it's on the right track," he said when asked about the Chelsea move.
Koulibaly has been in Naples since 2014 and has made 314 appearances for the club. That includes 34 appearances last term, scoring three goals.
It's not the first time he's being linked with a move to Chelsea, either, with the Premier League club seeing a bid of over £50m being rejected by Napoli back in 2017.
Now, five years later, Koulibaly looks like a leading contender to move to Stamford Bridge, however he's not the only player on the club's radar.
Presnel Kimpembe, Nathan Ake and Jules Kounde have also been heavily linked with a move to west London, however it remains to be seen whether a move will be finalised.
For Chelsea, the need to bolster their defence is of the utmost importance.
Following the conclusion of last term, Thomas Tuchel lost two star defenders in the shape of Antonio Rudiger and Andreas Christensen.
Rudiger completed a free transfer to Real Madrid, while Christensen left the Blues in favour of Barcelona, leaving a sizeable hole in the German coach's defence.
However, with Koulibaly emerging as the club's top defensive target, it means that efforts are very much stepping up to address the frailty at the back.