Napoli are looking to strengthen their midfield and have plenty of cash following the sale of Ezequiel Lavezzi to Paris St Germain.
Meireles impressed for a Chelsea side that won the Champions League last season.
The Mirror reports that Napoli president Aurelio De Laurentiis has made enquiries to Meireles’ agents about a move.
Meireles said: “I am focused on the Euros and cannot think about my future now.”
