The full-back is reportedly keen on a move away to earn back his France spot ahead of Euro 2016.
The defender is currently a back-up option at the Emirates, with youngster Hector Bellerin occupying the right-back position for the Gunners so far this term.
The Spaniard was employed in the role last season as Debuchy spent a period out injured and has impressed to such a degree that manager Arsene Wenger has stuck with him this campaign as well.
That has led to the Frenchman to seek an exit, with him also having lost his place in the France national team, something he is keen to reclaim with Euro 2016, which the France are hosting, coming up next summer.
To do that, though, he will need to be playing regularly and Roma could be a solution should a move be the only option for the Arsenal defender, according to France Football.
Manager Rudi Garcia would be interested in his services should he be made available, with him keen to keep improving his squad as they aim to challenge for the Serie A title.
That is something that would surely attract Debuchy, who would be almost be guaranteed first-team football in the side if he leaves Arsenal.