Unconfirmed reports suggest that Liverpool attempted to renegotiate the fee late on after a problem was flagged up by the medical - believed to be involving Fekir's knee and his past injury problems.
The Reds were expected to complete a deal for the 24-year-old former Saint-Priest frontman.
L'Equipe report that were not completely satisfied with the results of the medical and attempted to renegotiate Fekir's valuation with Lyon.
Fekir is one of the best attacking players in Europe who would be a great signing or Liverpool in the summer transfer window.
"It's always like that when you talk about a transfer: each tries to raise his price, to lower his price, when there's a hiccup someone wants it reduced".
He has won a place in the France World Cup squad for his performances, though Antoine Griezmann is set to be preferred to him in the starting XI for Saturday's final warm-up friendly against the USA.
A five-year deal, worth more than £140,000 per week, has been agreed and Liverpool's medical team travelled on Friday to Paris to conduct a medical at France national team base in Clairefontaine.
"The transfer has not been done and even less so at this price", Jean-Michel Aulas, the Lyon chairman said in a message to l'AFP.
"Although Liverpool have been Nabil's priority among a number of offers from ambitious clubs, Lyon are overjoyed that they can count on the presence of their captain, who will be a significant part of their 2018-19 season as they enter the Champions League after finishing in third".
Fekir, who scored 18 goals and made a further eight, is now in preparations with France ahead of the 2018 Russia World Cup.