Metro reports that the Nerazzurri are planning to make an £8million bid for the 27-year-old defender.
Vermaelen might be persuaded to leave the Gunners in January in order to get regular first-team football.
Vermaelen suggested last month that he might have to leave Arsenal in order to ensure a place in Belgium's World Cup squad.
"He is rightly frustrated because he has the quality to play, because he behaves with a fantastic attitude and is a credit to our job. I can understand completely his frustration," Arsenal boss Arsene Wenger said after the game against Crystal Palace.
Vermaelen's current contract with the Gunners is set to expire in the summer of 2015.