Debuchy's future at Arsenal has been in question for more than a year following the emergence of Hector Bellerin as the Gunners' first-choice right-back.
Debuchy is set to return to training today following a hamstring injury but looks set to leave the club before Tuesday's transfer deadline.
And the Daily Mirror claim the 31-year-old is angling for a move back to his native France.
Chelsea and Arsenal squads enjoy team meals out, but where is Mesut Ozil?
Wed, January 25, 2017
Chelsea and Arsenal both enjoyed team meals out ahead of their FA Cup games this weekend, but Mesut Ozil was mysteriously absent from the Gunners' dinner
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Chelsea and Arsenal both enjoyed team meals out on Tuesday evening
According to the report, Debuchy is keen to get going and has been told he is free to seek a new club.
Arsenal manager Arsene Wenger yesterday confirmed both Debuchy and Carl Jenkinson – wanted at Crystal Palace – face competition for places.
“I didn’t close the door because there’s a lot of competition on the right flank," Wenger said.
Arsenal right-back Mathieu Debuchy could leave for France this month
Debuchy is expected back at Arsenal training today
Debuchy (left) has played just 16 minutes of football all season
"Now Gabriel has been convincing on the right side as well, so I don’t close the door.
“What I just want to say is he (Debuchy) is fully fit now and so he is available to play and maybe even to have an experience somewhere else.”
Debuchy spent the second half of last season on loan at Bordeaux in an attempt to boost his Euro 2016 selection chances – but he did not make the cut in Didier Deschamps' France side.