The French side could rival Roma for the player's signature in January.
The French defender is expected to leave the Gunners in the January transfer window, with him having struggled for game time this season and last.
That is because Hector Bellerin has continued to impress in the side, continuing the fine form he has showed since breaking into the first team last season.
Debuchy has been unable to supplant him, and is keen on a move away to keep his hopes of going to Euro 2016 with the French national side.
That desire to leave has caught the attention of Lyon, who are interested in securing the former Newcastle United defender according to the Daily Mail.
They face competition for his services though, with Serie A side Roma still being credited with an interest in his services.
Arsene Wenger may disappoint them yet though, with him unlikely to sanction a sale unless he has sufficient cover in his squad as they eye a Premier League title come the end of the season.