The Tigers are looking for a right-back after Moses Odubajo's injury.
The Gunners full-back has been linked with a departure from the Emirates Stadium this summer after falling down the pecking order over the last two years.
Hector Bellerin has firmly established himself as first choice in Arsene Wenger’s side while Calum Chambers is ahead of the Frenchman as back up.
Indeed, Debuchy is more than aware of his chances being limited and headed out on loan to Ligue 1 side Bordeaux in the search of first-team football at the end of last season.
A permanent exit is looking likely this summer, with several sides in Europe already linked with making a move. And according to the Daily Mail, Hull are another club who could be chasing his signature.
They have been hit by injuries of late, with Alex Bruce facing a spell on the sidelines with an Achilles injury and Moses Odubajo suffering a dislocated knee in a friendly at Grimsby Town.
And that could lead to manager Steve Bruce to looking at a move for Debuchy in his search for a replacement right-back.