Liverpool manager Jurgen Klopp has reportedly made the 24-year-old his top summer transfer target and is keen to wrap up a deal before he goes off to the World Cup with France.
Fekir has admitted that he could be tempted by a move away from boyhood club Lyon this summer, with the 'Reds' the outright favourites in the face to sign him.
According to French publication 'L'Equipe', talks between the two clubs are already underway, with Klopp having met the player to explain his vision for how he would fit into the side at Anfield.
Liverpool are keen on adding another attacking option to their ranks, with the dip in their performance following Mo Salah's withdrawal in Saturday's Champions League final defeat to Real Madrid clear for all to see.
Lyon are believed to be holding out for around £53m (€60m) for the man who scored 23 goals in 40 games in all competitions this season.