The Gunners have been linked with the former Stoke City and Blackburn midfielder for some time, following two great years in La Liga.
N’Zonzi is reportedly looking for a move away from Sevilla ahead of the new season, as he looks to challenge himself and develop elsewhere.
Wenger is a long-term admirer of the Frenchman, and has been monitoring his progress closely in Spain over the past two seasons.
N’Zonzi recently had the chance to show the Gunners boss what he can do first-hand in the Emirates Cup, in Arsenal’s 2-1 defeat to Sevilla.
The 28-year-old performed well in the match in north London, even bagging a goal in the away side’s unlikely victory.
It remains to be seen whether Wenger will indeed make a move for the central midfielder, who is believed to have a €40 million release clause.
Juventus are also reported to be considering an approach.
Gunners legend Perry Groves recently spoke out about N’Zonzi, suggesting he would be a great buy for his former club.
“I’ve been a massive fan of Steven N’Zonzi,” Groves told sports.bwin.
“I think he could do a real job in the centre of that midfield for us, adding the steel he did at Stoke and Blackburn. He’s a destroyer.”
On Arsenal’s other potential deals, he added: “I think the [Thomas] Lemar deal will get done, it’s coming down to how much.
“I’d like to think we’re in the position that if they want £45million, then we go and pay it and send the right message to the player that we want you.
“As mentioned, I still think we’re two or three players away from winning the title.”
It seems there are more than a few Arsenal fans who agree with Groves’ original point, with many calling for Wenger to sign N’Zonzi.