Cole has failed to impress Liverpool boss Brendan Rodgers since returning from his loan spell in France.
"It is not easy for him because he does not play much," the former Lille midfielder told L'Equipe.
"It worked well for him at Lille. Maybe would be a good idea for him to return there.
"The club, the coach, the fans love him at Lille. I've heard that Rudi Garcia would be interested to have him back."