The midfielder has made only two starts under Brendan Rodgers' new-look team, including a midweek run out against Swansea in the Capital One Cup, when the Welsh side defeated the Reds 3-1 at Anfield.
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Ahead of Liverpool's home game against Newcastle on Sunday, the Magpies' midfielder told The Mirror: “It’s difficult for him [Cole] because he’s not playing so much.
“He did well for Lille and maybe it would be a good choice to go back. He is not playing a lot with Liverpool, so if he wants more games, he can play more there.“They like him at Lille – the club, the manager and the fans. I heard manager Rudi Garcia was keen to take him back.”
Cole made 38 appearances whilst on loan to the French club, in contrast to his fringe status back at Liverpool.