The Lyon forward is one who many top European clubs have been assessing.
While he has not moved yet this summer, L’Equipe states that a late Reds offer may change his circumstances.
The source adds that Cherki has not made up his mind to leave the Ligue 1 side.
Cherki is weighing up the possibility of leaving or signing a new contract with Lyon.
Liverpool may be ready to enter the fray, with Lyon valuing the forward at €15 million.