The Spaniard has been monitoring Vermaelen's contract situation at Arsenal during the last few months as it has looked more and more likely that the Belgium international would leave the Emirates Stadium at the end of the season.
Vermaelen is likely to have a number of options in the summer if he is to leave Arsenal, as he is an established international defender who is capable of playing at either centre-back or left-back.
The 28-year-old has been unlucky this season as he has been unable to break up the reliable partnership of Laurent Koscielny and Per Mertesacker.
Vermaelen will be able to prove to his potential suitors that he is still capable of representing a top team at this summer's World Cup as he is still expected to play a leading role for Marc Wilmots' side.
The former Ajax man is expected to end his five-year spell at the north London outfit after starting just seven Premier League games during this season's league campaign.
Napoli would have to pay a small fee for Vermaelen if he did decide to leave Arsenal as his current deal is due to expire next summer.