The Gunners chief believes he can persuade the Spain number one to join the club following Carlo Ancelotti's decision to retain Diego Lopez as the starting keeper for Real Madrid on the opening day of the La Liga season.
Former-Madrid boss Jose Mourinho first benched Casillas last season, and Ancelotti has retained faith in Lopez.
And the report claims Wenger is keen to find a replacement for current first-choice stopper Wojciech Szczesny after the Pole's error-strewn performance against Aston Villa on Saturday.
Szczesny has been unconvincing for the past 18 months, and Wenger - who is coming under increasing pressure from Arsenal fans to spend money - is targeting a new keeper before the transfer window closes.
Casillas is reportedly 'unsettled' at the Bernabeu and unhappy at his current role on the bench heading into a World Cup year.
The Spain stopper is still regarded as first choice by national team coach Vicente Del Bosque, but wants playing time to hold off a challenge from Victor Valdes as the squad prepares to defend its title in Brazil next summer.
Arsenal are willing to offer up to £8m for the 32-year-old, but the report claims the Gunners believe Real Madrid will not entertain offers below £15m.
The north London club are yet to spend a single pound this transfer window, and Wenger was the target for chants of 'spend, spend, spend' during Arsenal's shock 3-1 home defeat to Villa at the weekend.
They've already missed out on the likes of Gonzalo Higuain and Luiz Gustavo, while reported interest in QPR stopper Julio Cesar has failed to materialise.