The Azzurri started the season magnificently but Rafa Benitez has seen his side falter a little in recent weeks.
Owner De Laurentiis has indicated that he is ready to bring in at least two new faces and the defence is a priority.
Liverpool's Danish defender Daniel Agger has been identified as a target but if Italian press reports are to be believed, Arsenal man Vermaelen could be the preferred signing.
Napoli representative Maurizio Micheli was present at Arsenal's game against Chelsea yesterday and the Corriere dello Sport insists he was there to discuss Vermaelen's future.
Vermaelen hasn't had the first-team opportunities he wants for Arsenal this term and there have been suggestions that he could welcome a fresh start, even if just on loan.
The paper believes that Agger remains on Napoli's radar as well as Mateo Musacchio of Villarreal, Nicolas Nkoulou who plays for Marseille and Saint Etienne's 19-year-old Kurt Zouma.
image: © Ronnie Macdonald