The France international has not featured for the Gunners since November and has emerged as a target for a number of struggling Premier League teams
The Sunderland manager is looking to bolster his relegation threatened side with several new additions before Monday’s deadline and confirmed he had made an enquiry for the France international.
Debuchy has not featured for Arsenal since November but with Hector Bellerin the club’s only other recognised right-back, Allardyce believes his old foe Wenger will be reluctant to do business.
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He said: “I am not sure he wants to leave Arsenal or that Arsene Wenger would sell him.”
Sunderland are currently in 19th place in the Premier League - they sit four points from safety - and Allardyce’s hopes of snapping up Andre Ayew from relegation rivals Swansea have also been dashed.
He said: “Have we given up? Yes. I can’t see Swansea selling. I never thought they would.
“We never put a bid in. It was a bit more speculation whether Swansea would let him go or not.”