The right-back found game time hard to come by at the Emirates Stadium this term after picking up an injury as the form of Hector Bellerin has been so impressive.
The France international has since been loaned out to Bordeaux, and the 30-year-old has confessed he may be forced to move on a permanent basis.
“A future at Arsenal? It’s difficult, there’s a young guy who’s 20 in my position who is playing good matches,” Debuchy told beIN Sport.
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“My future could be in France.”
Arsenal boss Arsene Wenger admitted earlier on Friday that he rebuffed an offer from Manchester United in the January transfer window for Debuchy as he did not want to strengthen a rival club.
Meanwhile, the defender has been impressed with what he has seen at Bordeaux so far.
“I’ve found a really young team,” he told the club’s official television channel. “There are a lot of youngsters here with a lot of talent.”
Debuchy has played in all three of Bordeaux’s Ligue 1 encounters since making the jump to France at the end of the January window.