Despite this, Goal understands Liverpool believe a deal can be thrashed out before Fekir flies to Russian Federation with his national team this weekend.
Looking to bounce back from the disappointment of losing the Champions League final last month, Liverpool have already bolstered their midfield options for next season with the arrivals of Fabinho from Monaco and Naby Keita, in a deal agreed with RB Leipzig last summer.
Fekir will be given permission to leave France's World Cup training base and could undergo his medical on Merseyside on Friday.
Serena Williams quits French Open clash with Sharapova due to injury
She will await the victor of Monday's match between Spaniard-Venezuelan Garbine Muguruza and Ukrainian Lesia Tsurenko . I can only take solace in the fact I'm going to continue to get better.
Lyon president Jean-Michel Aulas appeared to rule out Liverpool's chances of signing Fekir before the tournament in Russian Federation and the Reds feared the French club were using the World Cup to ramp up the price for the midfielder.
The Independent report that Aulas believes that Liverpool will have to calculate the potential of summer performance into their offer.
The Swiss winger was part of the Stoke City side relegated last season and has been clear about his plans to exercise a relegation release clause written into his contract with the Potters.
Bayern Munich and Atletico Madrid are also reportedly interested in the French global - but Liverpool are now in the driving seat.