The 17-year-old winger is one of the most highly-rated young players in France, and the report claims he's already attracted interest from the likes of Porto, Juventus and Benfica.
But Arsenal are also in the hunt for Nkoudou, who is thought to have a £1m release fee clause in his Nantes contract.
The Gunners are expected to draft in reinforcements this month, as Arsene Wenger's side look to clinch a Champions League qualification spot.
But Nkoudou would be one for the future. Arsenal already have Alex Oxlade-Chamberlain, Lukas Podolski, Gervinho and Theo Walcott in wide areas - so Wenger has plenty of options for the time being - and there is thought to be no rush to make a move.
Arsenal face Swansea in their FA Cup third round replay this evening after the first match ended 2-2 at the Liberty Stadium. The tie, at the Emirates Stadium, comes three days after the Gunners slumped to a 2-0 home defeat to Premier League champions Manchester City.
But Wenger has revealed he will not rest Jack Wilshere for the match.