It could be just a minor hitch but rumours are circulating it could be due to the player's injury record, with Fekir suffering a serious knee injury three years ago.
The 24-year-old's switch to Merseyside was expected in the coming days with contract talks ongoing between the English club and Lyon.
This comes on the back of FFF's President's comments that Fekir had gone through a medical and the outcome of the same was "positive".
"This does not prevent him from being very concerned by the France team".
'Olympique Lyonnais informs that the tripartite negotiations with the Liverpool club and Nabil Fekir for the transfer of the captain of OL have not succeeded and that Olympique Lyonnais has chose to put an end to this negotiation tonight at 20:00, ' a statement read.More news: USA must stop separating migrant children from parents
"He passed his medical in Clairefontaine".
Consequently, the Reds were hoping to negotiate a lower fee which prompted Lyon to pull the plug on any potential deal. That's logical, we've done it for other players.
Fekir, who scored 18 goals and made a further eight, is now in preparations with France ahead of the 2018 Russia World Cup. "It would be better for him [to complete the transfer], but he's not perturbed", Le Graët added.
Le Graet, speaking in Lyon a few hours before France played the United States in a World Cup warm up game in the city, said: "These are negotiations".
However, negotiations have now hit a snag and the prospect of another season in Ligue 1 beckons for the highly exciting attacking midfielder, whose 18 goals and eight assists propelled Bruno Genesio's side to third place this term, two points behind runners-up Monaco.