But the 30-year-old's first season at the club was disrupted by injury, with problems with his ankle ligaments and a dislocated shoulder limiting him to just 11 Premier League starts.
He has featured just once this season, in the Gunners' 2-0 loss to West Ham United in their first league match of the campaign, with the impressive 20-year-old Bellerin keeping him out of the side.
The Spanish youngster also received his first call up to the national squad this week.
"It is difficult," Debuchy told L'Equipe.
"Even if I had not played a lot last season, in my head I would return to start after my recovery.
"But, at the Community Shield against Chelsea, Wenger chose him, Bellerin," he added.
"It was a surprise and a disappointment. Let's say it (leaving) crossed my mind ... But I want to be at Arsenal and to take my place," L'Equipe quoted the player as saying.
The right-back is currently training with the France squad ahead of their friendlies against Portugal and Serbia.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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