The French champions are keen on the 26-year-old Uruguayan, who scored 29 goals in Serie A last season, and are reported to have opened with a bid of £43m.
However, Partenopei chairman Aurelio de Laurentiis is adamant on seeing Cavani's £54m release clause met before allowing him to leave.
"We presented De Laurentiis with an offer that I consider really interesting," the Brazilian told Il Mattino.
"The negotiations continue. We will remain in contact and in these next few days there could be news."
Cavani arrived in Naples in a £12m deal from Palermo in 2010.