Pépé is in big demand this off-season after firing home 22 goals in Ligue 1 last season and reports in France claimed that the Reds are in the box seat to do a deal.
Manchester United and Bayern Munich are also in the hunt but French publication Le10Sport claimed that Liverpool have jumped ahead of their rivals by making a £72 million bid.
That could be enough to convince Lille to cash in on their star forward, and now it remains to be seen if either United or Bayern will come in and match it.
Lille have accepted that the Ivory Coast ace is set to move on but it is no surprise that they will try and get as much as possible for him.