Fekir had been on the verge of a £53m switch to Anfield last weekend, selecting his shirt number and conducting interviews with the club's in-house media team before the move broke down following concerns over an underlying knee problem.
Liverpool are now understood to have moved on to other options, but The Mirror reports that there could still be hope of resurrecting the deal if Lyon president Jean-Michel Aulas softens his stance.
Aulas has repeatedly stated his desire to keep Fekir and pulled out of negotiations after Liverpool attempted to restructure the transfer fee when the knee problem came to light.
However, the 24-year-old is desperate to join Liverpool and Aulas could still perform a U-turn in order to cash in on the wantaway attacker this summer.
The Lyon president is expected to wait until after the World Cup to make a final decision, though, as he hopes that Fekir enjoying a successful tournament will create a bidding war between the likes of Liverpool, Bayern Munich and Atletico Madrid.