According to the Daily Express, Wenger has turned to the Dutch international who has been pursued by Manchester United boss Louis van Gaal. Van Gaal worked with Vlaar with the Netherlands national team.
The Arsenal boss has put aside £8m to bid when the January transfer window reopens in just over a month's time. And the Gunners are willing to offer to improve Vlaar's £25,000-a-week wages in an effort to encourage him to join the north London club.
While United are also short at the back, Wenger has clearly taken the view that his defence cannot continue to operate as it currently stands. The Arsenal boss has been forced to play Nacho Monreal at centre-back.
Injuries to Mathieu Debuchy, Laurent Koscielny and the sale of Thomas Vermaelen to Barcelona without first signing a replacement has left Wenger short of options.
At United, a number of academy players including Tyler Blackett and Paddy McNair have been drafted in to cover for injured first-team stars like Marcos Rojo and Phil Jones.
In the middle of this tug of war is Aston Villa, a club in difficulty at the wrong end of the table and with a manager, Paul Lambert, who has already reiterated his desire to hold on to his best players in the January window.
Vlaar's contract situation
But his hand may be forced with Vlaar's contract running down. He can speak to other clubs from January as his Villa deal expires at the end of this season.
Van Gaal was believed to be the frontrunner for his signature considering his Dutch connection, while the Old Trafford club are also lining up offers for Real Madrid's Raphael Varane and Athletic Bilbao's Aymeric Laporte as potential targets.