The Reds believe their name is being used to promote interest in the 23-year-old who is expected to make a big switch.
But the Evening Standard claim Liverpool have no interest in Pepe.
That’s because Jürgen Klopp is only looking to make small adjustments to his squad this summer after a successful season.
Liverpool won the Champions League, beating Tottenham in the final, and finished just one point behind Premier League champions Manchester City.
Pepe impressed for Lille this season, netting 23 goals and providing 12 assists in all competitions.
But the reports say Liverpool have no interest in the player.