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The Gunners would have to pay around £30m for the former Stoke man who is looking for an exit from the La Liga side.
N’Zonzi fell out with manager Eduardo Berizzo after the 3-3 Champions League draw with Liverpool earlier this season.
The Daily Express claim the industrial midfielder is Wenger’s top target for the upcoming transfer window.
With Sevilla sacking Berizzo though, the future of N’Zonzi might not be as clear.
Everton boss Sam Allardyce is also interested in him and will rival Arsenal for his signature.
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The Toffees manager brought N’Zonzi to England when he signed him for Blackburn in 2009 before he moved on to Stoke.
West Ham boss David Moyes is also interested in bringing the 29-year-old in this January.
Juventus are long-term admirers of N’Zonzi and could join the race for the France international too.
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Arsenal will be looking to sure up their midfield after the 3-3 draw with Liverpool on Friday.
The Gunners return to action against Crystal Palace on Thursday, December 28.