A €17m (£15.1m) bid was placed by the Swans, the French newspaper reports, but the offer was rejected out of hand with the Ligue One side demanding teams match the 26 year old’s €40m (£35.7m) buyout clause.
Roma attempted to sign the the Ivory Coast international earlier in the transfer window but were unable to match Nice’s demands for the player. The Gunners are believed to be the leading candidate to land Seri currently.
The central midfielder could be an ideal fit for Arsenal who are struggling in the middle of the park for attack minded players. With Santi Cazorla still out injured and Jack Wilshere destined to leave the Emirates, Seri is someone who could fill the void.
In 39 appearances last season, the midfielder scored seven goals and contributed nine assists, helping to guide Nice to a third place finish in the French league.