Italy's Tuttosport reports that Cavani is considering an extension on his current contract with Napoli.
The renewal would tie him to the club until 2018 and raise his wages to €7.5m per season.
The striker is currently in Brazil on international duty, where his Uruguay take on Italy in the Confederations Cup third place play-off.
He is clearly exasperated at the speculation about his future.
“At this moment everything is tense in Naples,” he told La Gazzetta dello Sport after criticising the media in his Press conference.
“Anything I say gets misinterpreted, so I prefer to stay calm. We’ll see what happens later on. Nobody knows what could happen tomorrow or in a year, so I just carry on with my mentality.”
The transfer speculation has been non-stop over the summer, as Chelsea, Manchester City, Real Madrid and PSG have reportedly all tried to sign him without reaching the €63m buy-out clause.
And Sport Mediaset claimed on Saturday that Cavani had agreed personal terms with Chelsea .
The Daily Mail also suggested that Chelsea have raised their bid to €52.5m, but it is still well below the €63m asking price.
Napoli president Aurelio De Laurentiis and coach Rafa Benitez have been adamant there will be no discount on the buy-out clause.