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.
"It's under negotiation, I think it will be done".
Lyon posted messages on social networking site Twitter making it clear that no deal has been agreed with with the Reds over the 24-year-old, who can also operate as a forward. "I spent 15 minutes with him this morning [Saturday], and he's anxious by the France team".
"He passed his medical in Clairefontaine".
"It's always like that when you talk about a transfer".
Now we must wait and see if Liverpool and Klopp go back in for a player they have coveted so much.
"Everyone tries to raise their price, to lower their price, and when a little issue flares up, it's part of the game".
The Merseyside outfit have funds to spend after the Reds sold Philippe Coutinho in a £142m deal from FC Barcelona in the January transfer window.
Fekir is coming off a career-best season with Lyon, in which he scored 23 goals and created eight more, leading the Parc OL side to a third-place finish in Ligue 1 behind Paris Saint-Germain and Monaco.
With France scheduled to play the United States tonight and then fly off to Russian Federation ahead of the World Cup, it now appears the 24-year-old will remain at Lyon, at least until after the tournament.