Reds boss Jurgen Klopp has kept a low profile in the transfer market this summer.
But winger Pepe’s availability has piqued his interest ahead of the new season.
The 24-year-old finished behind only Kylian Mbappe in the Ligue 1 scoring ranks last term with 22 goals.
And journalist Duncan Castles claims Liverpool have been in talks with Pepe’s agent over a possible swoop.
“Liverpool retain an interest in Pepe,” he said on The Transfer Window Podcast.
“They have not gone to Lille as yet to discuss terms, all of their work has been done on the player’s side, with the agent.
“I think Lille’s thinking here is once one big bid comes in, then they will see the strength of the other suitors.
“They clearly would like to have a bidding war.”
Manchester United are also pursuing Pepe, who had a quiet Africa Cup of Nations with the Ivory Coast.
And it seems the Red Devils are at a more advanced stage of negotiations than Liverpool.
According to a source close to him, United last week advanced a long-standing interest in the forward.
Pepe is valued by Lille at more than £70m and has three years remaining on his contract.
The Ligue 1 side’s president Gerard Lopez has been open about their intention to sell him to fund reinvestment in their squad.
Liverpool take on Sporting Lisbon in their next International Champions Cup clash early Thursday morning at 1.05am.
Manchester United take on Tottenham earlier on the same day.