The Uruguayan international, whose side were knocked out of the Confederations Cup by Brazil on Wednesday, is widely expected to leave Italy this summer, with Real Madrid, Chelsea and Manchester City all reportedly interested in him.
However, the 26-year-old is keen on speaking to club president Aurelio De Laurentiis to discuss his future in Naples.
"I love Naples. It's my town and my heart is there. But when I was here in Brazil, I heard untrue rumours and things about me," said Cavani.
"For this reason, now I want to talk as soon as possible with president De Laurentiis.
"We must clear ourselves. I'll talk with him as it's done between men really soon."
Cavani netted 36 goals in 41 appearances for Napoli last season.