The Serie A club has met with the agent of the Belgium defender, who has been kept out of the Gunners team by Per Mertesacker and Laurent Koscielny in recent months.
Benitez is a long-term admirer of Vermaelen, who has suffered due to the blossoming partnership between Per Mertesacker and Laurent Koscielny at the Emirates Stadium.
Zenit has also been linked with a move for the Belgian before the Russian transfer window closes on February 25, but Arsenal has no intention of letting him go mid-season.
Vermaelen, who has been sidelined with a series of niggling injuries since starting the Gunners' FA Cup win over Tottenham on January 4, has been a fringe player at Emirates Stadium over the last 12 months.
However, the Arsenal staff has been impressed by his attitude and professionalism, and the defender has not pushed strongly for a move even though his place in Belgium's highly competitive starting lineup at the World Cup is under threat.