Koulibaly is reportedly keen to find a new club this summer after failing to agree terms over a new and improved contract at the Serie A club.
His situation at the Stadio San Paolo has attracted interest from the Premier League, with Chelsea, Arsenal and Everton all said to be keen on his services.
And according to Italian outlet Mediaset Premium, Chelsea are set to offer £33.3million (€40m) for the Senegal international within the coming days.
The report suggests Chelsea's first move is likely to spark a bidding war for the 25-year-old's signature, with Everton willing to spend £46m on him.
Website Goal claims Arsenal are one of several major European clubs to have been offered the chance to sign Koulibaly and cite a £38m price-tag.
GETTY
Chelsea to make £33m bid for Kalidou Koulibaly
Arsene Wenger is thought to want a top class defender before the summer window shuts, but is yet to make a move for the sought-after Koulibaly.
Napoli are keen to keep hold of the centre-half, but are unlikely to resist the Premier League's spending power after signing him for around £6m two years ago.
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy