Seri, who moved to Nice from Portuguese side Pacos de Ferreira in 2015, impressed last season, helping his club to a third place finish in Ligue 1.
The 26-year-old has been linked with a move to the Premier League this summer with Arsenal and Tottenham touted as potential suitors.
ESPN claim both north London giants remain keen with the Gunners currently leading the way.
Arsenal scouted the Ivroy Coast international on several occasions last season.
It is said that Arsene Wenger is weighing up a bid for Seri before the close of the summer window.
And the reports add that tomorrow could be a big day in deciding Seri's future.
Nice are set to take on Ajax in their Champions League qualifier.
The two sides are currently locked a 1-1 after the first leg and ESPN suggest Seri will be more open to leaving Nice should they fail to make it into the Champions League proper.
Wenger has already completed deals for left-back Sead Kolasinac and striker Alexandre Lacazette this summer but has plenty of cash remaining.
The Gunners are still working hard to secure the services of Monaco winger Thomas Lemar but could move for Seri in the coming weeks.
Tottenham, meanwhile, are yet to make their first signing of the summer.
