The Belgium international is off contract in June and weighing up his options, with a return to Ajax mooted.
However, Sky Italia's Francesco Modugna says Vertonghen's situation is being actively discussed inside Napoli.
"Vertonghen is a name that has been buzzing around Naples in recent months. He would be an excellent addition to the club, but there is a risk of a bidding battle," said Modugna.
The journalist is referring to competition from Inter Milan, which are also keen on the stopper.