The Ivory Coast international is an in-demand player in the summer transfer window following his impressive campaign in Ligue 1.
Pepe, 24, made 11 assists and scored 22 times in Ligue 1 to attract interest from a host of top European clubs ahead of the transfer window.
Liverpool FC were thought to be uninterested in signing Pepe as the Reds prepared to have a quiet summer.
However, Lille president Lopez has now revealed that Liverpool FC have contacted Pepe’s representatives to sound out a deal.
“I know there have been discussions with the player, not with us as a club,” Lopez told RMC Sport.
“Liverpool have players in those positions and I read that maybe there were players who could leave, or not.
“I am not particularly focused on Liverpool. But it is true that there have been discussions with agents.”
Liverpool FC have only signed Dutch teenager Sepp van den Berg from FC Twolle in the summer transfer window so far.
The Reds allowed Alberto Moreno and Daniel Sturridge to leave the Merseyside club on a free transfer earlier this summer.
The Merseyside outfit lacked some depth last season and Jurgen Klopp will be eager to secure more options to bolster their chances of beating Manchester City in the title race next term.
Liverpool FC were 2-0 winners against Tottenham Hotspur in the Champions League final in Madrid last month.
The Reds finished in second place in the Premier League table and a point adrift of eventual champions Manchester City.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news