The prolific Uruguay striker, 26, is unhappy with rumours he's heard while on international duty at the Confederations Cup.
Cavani said: "I love Naples. It's my town and my heart is there.
"But when I was here in Brazil I've heard untrue rumours and things about me.
"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 has a £54m release clause in his contract but Chelsea have pledged not to pay more than £40m for his services.