RMC says terms between the two clubs were agreed on Tuesday. Debuchy has also agreed to the move.
The fullback will join ASSE on-loan to the end of this season.
Debuchy is eager to work with ASSE coach Jean-Louis Gasset, who was France assistant coach when the Gunners defender was part of the Les Bleus squad.
The experienced fullback wants to be playing consistently again to give himself a chance to win a place in Didier Deschamps' France World Cup squad.