The Frenchman is desperate to secure a move away from the Gunners in order to save his Euro 2016 spot.
A move to struggling Sunderland may make sense from a footballing perspective, but whether he would accept a switch to Wearside is another matter.
Debuchy played for their bitter rivals Newcastle United, leaving in 2014 to attempt to kick his career on with Arsenal, but he has been unable to establish himself.
Sunderland have already signed one ex Toon player this month, adding back up goalkeeper Steve Harper, who was a free agent.
Debuchy has been linked also with a switch to Aston Villa, but Sunderland have a better chance of staying in the Premier League than Remi Garde's side.
Newcastle have no need to re-sign Debuchy, with replacement Daryl Janmaat proving to be excellent, but seeing the defender join their rivals would be seen as a treacherous act by fans.
Here is a look at the reaction to the reports...
Mathieu Debuchy being touted by Aston Villa & Sunderland - how the might have fallen. Yet another who thought the grass was greener. #NUFC— Newcastle Stats (@NewcastleStats) January 26, 2016
Sunderland in for Debuchy... If he goes, there's no way he'll be let off like Harper! There will be an uproar. #NUFC— NUFC HQ (@NUFC_HQ) January 26, 2016