Reports suggest the Reds have made a formal enquiry about the Lille forward - a step further than interested Arsenal , Manchester United and Everton.
According to French outlet Le10 Sport, the Reds have established contact with Ligue 1 side Lille about the in-demand forward.
Pepe is wanted by a host of sides after the 23-year-old scored 19 times and provided 11 assists in 32 matches.
Jurgen Klopp knows his must add more to his forward options this summer.
Now, the reports claim, the Premier League leaders are hoping to get a deal done.
Pepe is second in the scoring charts to PSG superstar Kylian Mbappe and his form in front of goal has taken the club to new heights.