Chelsea owner Todd Boehly sees Koulibaly as the most affordable big name centre-half target on their shortlist.
The Mirror says the Senegal international has 12 months left on his contract with no agreement over a new deal on the horizon.
It means Napoli face needing to sell this summer with 31-year-old Koulibaly interested in a £40million move to Stamford Bridge and his representatives sounding out potential suitors.
Chelsea boss Thomas Tuchel is most keen on Juventus centre-back Matthijs De Ligt but has so far been scared off by his £102m buyout cause. Inter Milan's 27-year-old Slovak international, Milan Škriniar, would also cost upwards of £55m and is a prime target for PSG.
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