The playmaker is known to have his admirers in the Premier League, with Chelsea known to be keeping a close eye on his progress.
Seri is rated at around £40m by his current employers and saw a move to Barcelona collapse last summer and it is a former Barca employee who is heading Arsenal's interest.
Raul Sanllehi, currently working as Arsenal's director of football, spent 14 years with the Catalan side and is believed to have held talks with the player's representatives over a switch.
However, any move would depend on who is named Arsene Wenger's successor at the Emirates.
The 26-year-old is an Ivory Coast international and has made 30 Ligue 1 appearances for Nice this season as they ended the campaign in sixth place.