The midfielder, who was one of the standout performers in Ligue 1 last season, is a wanted man this summer and he is being tracked by numerous clubs.
Arsenal, Barcelona, Roma and Tottenham are all said to be monitoring the 26-year-old and he is expected to move before the transfer window slams shut.
Swansea have also shown an interest in Seri but, according to L'Equipe, their opening offer of £15m has been rejected.
That bid is said to be way below Nice's asking price for the Ivory Coast international, who has a release-clause of around £35m.