The Liverpool Echo report that the two clubs have finally hashed out a deal for the Frenchman, with a medical expected to take place on Friday.
According to The Guardian, "Fekir is due to undergo a Liverpool medical at Clairefontaine, the France national team's training base, before signing terms on Friday".
Despite this, Goal understands Liverpool believe a deal can be thrashed out before Fekir flies to Russian Federation with his national team this weekend.
Fekir's proposed arrival would be the latest ambitious statement from the Champions League finalists after the £39m signing of Brazilian midfielder Fabinho from Monaco, and with Naby Keita arriving from RB Leipzig in July in a deal worth £52.75m.
These are clearly exciting times for fans and players involved with Liverpool and it looks like it could just be the beginning of a busy summer for The Reds.
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.
Klopp and co. hope to complete the transfer before the commencement of the FIFA World Cup, next week.
Liverpool are looking to clinch the £60 million (€68m/$80m) signing of Nabil Fekir before he heads off to the World Cup with France.
A fourth transfer could soon be on the cards with reports claiming a £12m deal for Stoke's Xherdan Shaqiri could be in the pipeline.
Fekir has also drawn interest from Chelsea and Bayern Munich, but Liverpool have been aggressive in chasing his signature.