The Gunners have been linked with a potential swoop to sign the Ivory Coast international in the current transfer window.
Seri was close to a move to FC Barcelona last summer but a deal failed to come to fruition and the Ivorian remained at Nice.
The 26-year-old has been touted with a potential switch to the Premier League this summer following another impressive campaign in Ligue 1.
Arsenal and Chelsea FC have both been linked with a swoop to sign the versatile African star to bolster their respective midfields.
Alternatively, Manchester City retain an interest given the stagnating discussions with Napoli over Italy international Jorginho.
Sky Sports News reporter Sheth believes Seri is unlikely to end up at Arsenal given the increased competition.
“He is a player who the Arsenal heirarchy have been long term admirers of. Seri is in talks with Napoli,” Sheth told the Transfer Talk podcast.
“He says he is tempted to wear the jersey. Seri’s preference is to play in the Premier League. Chelsea FC are interested. Man City are keeping tabs… It is looking less like he will move to Arsenal.”
Arsenal finished in sixth spot in the Premier League table last term to miss out on Champions League football.
The Gunners have signed veteran Switzerland international Stephan Lichtsteiner from Serie A giants Juventus earlier this month.
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