The 32-year-old joined Arsenal in 2014 but quickly fell out of favour with manager Arsene Wenger and went on to make just 13 Premier League appearances for the club during his three-and-a-half-year spell.
Debuchy eventually secured an exit when he joined Saint-Etienne during the January transfer window, and he admitted that he was "angry" at Wenger for not allowing him to leave the club earlier - particularly when United came calling.
"I would have liked to have left Arsenal earlier and to have played for a different club," he told RMC Sport.
"There were moments when I was angry with the manager. There was an approach from Manchester United and he did not want me to leave."
Debuchy made just 30 appearances for Arsenal across all competitions, scoring two goals.