Since arriving from Newcastle United in 2014, Debuchy has featured on just 23 occasions for the Gunners, with his last appearance coming against Bournemouth on November 27.
The Frenchman is deemed surplus to requirements at the Emirates Stadium and according to L'Equipe, Marseille are looking to take advantage of his situation.
While the full-back has two years remaining on his contract, the Ligue 1 outfit feel that they can tempt Arsenal into releasing the 32-year-old from his deal.
Debuchy is keen to secure regular first-team football during the upcoming campaign in an attempt to regain his place in the France squad should they qualify for the World Cup.
Part of Debuchy's time at Arsenal was spent on loan with Bordeaux, where nine starts were made during the second half of the 2015-16 season.