The Gunners boss is keen to tie Bacary Sagna down to a new long-term Arsenal contract, but is preparing contingency plans should the Frenchman fail to sign a new deal.
Wenger reportedly instructed Arsenal scouts to monitor Basta, who joined Udinese in 2008. The Serbia international has made over 50 league appearances for the Serie A side, and his versatility is something Wenger is thought to value.
Basta can operate at right-back or on the wing, and the 28-year-old has caught the eye with some impressive performances in Italy.
But Wenger's priority remains securing the future of Bacary Sagna. The French international has been out of action since breaking his leg in the final home match of last season against Norwich.
That injury ruled him out of Euro 2012, and the opening months of this campaign, but Arsenal youngster Carl Jenkinson has deputised ably for his teammate so far this year.
The former-Charlton trainee has looked solid at right-back, leading to reports that Sagna could be offloaded, with Inter Milan reportedly interested. But Wenger is unlikely to want to lose a player he once described as "the best right-back in the Premier League."