The former Athletic Bilbao No. 1 has been relegated to reserve goalkeeper at Stamford Bridge with Édouard Mendy the first choice.
Meanwhile, Napoli boss Luciano Spalletti saw his first-choice goalkeeper David Ospina leave this summer.
And Alfredo Pedullà reports Napoli have been speaking to Chelsea about a possible to deal for Kepa.
However, the player’s €7 million-a-year salary would be a sticking point and the Partenopei would require a contribution from Chelsea to ensure any deal, the report adds.
The report also suggests Alex Meret, who joined Napoli from Udinese in 2018 and was part of Italy’s victorious Euro 2020 campaign, remains the future goalkeeper of the club and is likely to sign an extension soon.
Chelsea and Napoli enjoy a positive relationship, according to the report, due to past dealings which saw Jorginho and Maurizio Sarri move to Stamford Bridge in 2018 while Kalidou Koulibaly joined the Blues this summer.