Talks are reportedly underway between officials of both clubs over a £60m move with Reds boss Jurgen Klopp eager to do his summer transfer buisness before the start of the World Cup next month.
The 24-year-old enjoyed arguably the best season of his career in 2017-18 as he helped Les Gones to finish third in Ligue 1, netting 18 goals and providing eight assists in the process and he is currently with France as they prepare for the 2018 World Cup.
Fekir's top-level performances have seen him linked with a number of clubs across Europe but Liverpool are at the front of the queue.
Fekir himself is not giving anything away and, when asked about his future, he said recently: "Will I sign anywhere before the World Cup? Honestly, I don't know."