Bacary Sagna has been first choice in that position for the Gunners since signing in 2007, but the Frenchman's contract expires at the end of this season.
With Sagna yet to enter talks over a new deal Wenger has begun the process of planning for his potential exit by sending scouts to watch Genoa full-back Vrsaljko, according to The Mirror.
Vrsaljko only signed for Genoa in July, after making his debut for the Croatian national side at the age of 19.
The 21-year-old has missed just one of Genoa's first seven league games this season, reportedly attraction early attention from Inter Milan with a quick transition to life in Serie A.
Wenger is not thought to have given up hope of persuading Sagna to stay in North London, but wants strong competition for Carl Jenkinson in that position should his efforts fail.