The Gunners chief is keen to bolster his squad in an attempt to secure a top four finish, and qualification for the Champions League.
Anderlecht’s Biglia is thought to be his top target, after the Argentine admitted that he is looking to move on.
Newcastle and Norwich are also thought to be looking at the deep-lying playmaker, but it’s thought that he would favour a switch to North London.
Wenger is also said to considering Wigan’s James McCarthy and Mohamed Diame of West Ham, but favours Biglia due to his range of passing.
Napoli winger Vargas has previously been on the Frenchman’s list of targets, with his the Italian club believed to be willing to allow him to leave in January on loan.
The 23-year-old Chilean was once dubbed one of the rising stars of world football, but has struggled for game time in Naples of late.
He is comfortable playing in a wide midfield position or just behind the main striker, which would allow him to fit into Wenger’s first-team plans.
Meanwhile Fulham are confident of agreeing a loan deal with Andrey Arshavin, who has been strongly linked with Reading.