The Reds came close to acquiring the Lyon forward in 2018, but complications with the player’s medical scuppered a £53m move.
And Jurgen Klopp will not be returning with a second offer for the attacking midfielder, despite the fact he has only 12 months remaining on his Lyon deal.
Fekir scored 12 goals in all competitions last season, having struck 23 times in 2017/18.
Lyon are reportedly willing to cash in one of their prized assets for £45m given his contractual situation.
But Fekir will not be playing his football at Anfield next term, with Liverpool set to look elsewhere for attacking reinforcements.