The Frenchman has fallen down the pecking order at the Emirates due to injury problems and lack of form.
In total, since his 2014 switch from Newcastle United, Debuchy has made 23 appearances for Arsenal, and only one of those outings was during last season.
According to The Mirror, the North London outfit are keen to clear the squad of deadwood, and Brighton have emerged as a potential destination for the right-back.
It is believed that Debuchy has been told that he can leave the club for free if a suitor is willing to take on the remainder of his contract.
The Frenchman, who cost £12m three years ago, played just 16 minutes of action in the 2016-17 campaign before he suffered a hamstring injury.