The France international has been linked with a move to the north London side since Unai Emery took over the reins from Arsene Wenger back in May.
The Gunners manager appears to targeting the middle of the park as an area that needs significant improvement ahead of the new Premier League term.
Arsenal tied down Switzerland international Granit Xhaka to a new long-term deal despite failing to convince since his £33m move from Borussia Monchengladbach in 2016.
Emery has also wrapped up a deal to sign the French midfielder in a £26m deal to sign Uruguay international Lucas Torreira from Serie A outfit Sampdoria.
N’Zonzi played under Emery for one season following his move to Sevilla from Stoke City in 2015 before the Spanish head coach took over PSG.
Sky Sports News reporter Sheth believes Arsenal will need to offload some players to fund a swoop for the France midfielder.
“They are in talks with Sevilla. It makes sense,” Sheth told the Transfer Talk podcast. “He managed N’Zonzi in his final season in charge.
“They have a limited transfer budget. To fund a big signing of someone like N’Zonzi who would command a fee of £20m or £30m, there would have to be some departures first to fund a move for someone like N’Zonzi.”
Arsenal have snapped up four new players in the summer transfer window after Torreira completed a switch to the Gunners.
The north London side have already signed Juventus defender Stephan Lichtsteiner, Bayer Leverkusen goalkeeper Bernd Leno and Borussia Dortmund defender Sokratis Papastathopoulos.
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