The Reds have long been in pursuit of the France international and were in talks over a £60 million (€68m/$80m) transfer deal with Lyon.
Despite the Ligue 1 side's assertion that a deal was not in the works, Fekir seemed Anfield-bound when French FA president Noel Le Graet said he had completed a medical at the national team's facilities during their preparation for the World Cup.
Lyon president Jean-Michel Aulas insisted this week that Fekir's future would be decided after the World Cup, but the French club have since stated he will be playing in Ligue 1 next season, as a breakdown spiked a deal.
"Olympique Lyonnais informs that the negotiations with Liverpool and Nabil Fekir for the transfer of the captain of OL have not succeeded and that Olympique Lyonnais has decided to put an end to negotiations tonight at 20:00," a statement read.
The change is thought to have centred around the 24-year-old's medical, as the clubs had reached an agreement for him the previous day. The Lyon captain suffered a knee injury in February which kept him out for six weeks and may have caused doubt.
Lyon's statement added: "Although Liverpool made the possible transfer of Nabil a priority, and [we have been] subject to other proposals consistent with the interests of Nabil and OL from ambitious clubs,
"Olympique Lyonnais is delighted soon to be able to count on the presence of our captain, who is a leading player for this 2018-19 season, during which the club will play the Champions League as a third seed."
Fekir scored 18 goals and made eight assists in 30 top-flight games for Lyon last season and is contracted to the club until 2020.