Ivory Coast ace Seri is available for £35million this summer thanks to a release clause in the 26-year-old's contract.
London rivals Chelsea are also interested in the midfielder, who is rated at around £40million and almost signed for Barcelona last summer, and are monitoring developments.
If the report is anything to go by, Chelsea are now leading Arsenal in the player's pursuit, even though the Gunners are in talks with Nice over a possible move.
The Ivorian has enjoyed another impressive campaign and attracted Premier League interest with a potential transfer fee of £40million being touted. He has made 30 appearances in Ligue 1 this season and scored twice, as Nice finished sixth.
Conte's future is up within the air after an underwhelming title defence, although the Stamford Bridge membership nonetheless have the chance to complete the marketing campaign with some silverware within the FA Cup last towards Manchester United this Saturday. Part of this overhaul is likely to see Jack Wilshere move away from the North London club, which would open up a slot in midfield, making Seri a viable target to replace the Englishman.