They could easily be seen as saving face with their fans having been prepared to sell their captain, and it could well be Liverpool who have backed out of a deal they are not happy with every aspect of.
On Saturday, French Football Federation chief Noel Le Graet suggested that Liverpool had attempted to lower Fekir's asking price.
Liverpool offered no indication as to the nature of the problem, although Fekir sustained a serious injury to his right knee when playing for France three years ago.
He said on Saturday: 'I saw him this morning for 15 minutes.
"It's under negotiation, I think it will be done".More news: LeBron James compares Warriors to Patriots after Game 3 of NBA Finals
And Hislop insists that the transfer saga is far from over, predicting that Fekir will eventually finalise a move to Liverpool.
Lyon president Jean-Michel Aulas is notoriously tough in transfer business but it is my understanding the deal has not fallen down because Liverpool tried to renegotiate the terms of the deal.
France forward Fekir has always been linked with a big-money move to Anfield and enjoyed a stellar campaign in France's top flight this season - scoring 18 goals and supplying a further eight assists.
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. There has also been some speculation that the Frenchman may move after the World Cup, but Lyon's actions today have made that seem less likely.
British and French media have been reporting for several days that the 24-year-old, who is part of France's World Cup squad, was on the verge of joining Liverpool for 60-70 million euros (USD 71-82 million).