Fekir has undergone and passed a medical at France’s training base Clairefontaine, according to RMC Sport.
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And it is understood his transfer will be announced today.
The deal is expected to be confirmed once the stock market shuts in France at 4pm BST.
Lyon earlier denied Fekir was on the brink of joining Liverpool today, however it is understood the Premier League club remain confident a deal will be agreed.
Fekir is Liverpool’s top target for the summer and the fee will be £48m rising to £53m.
Get French Football tweeted: “French stock market regulations state that a listed company, like Groupe OL, cannot release “important” information when the market is open, meaning any possible Nabil Fékir to Liverpool announcement will not occur before 17:00 English time, when the French stock market closes.”
However they have not accounted for the time difference between France and England meaning a deal could be announced at 4pm here, which is 5pm in France.
Fekir will become Liverpool’s third summer signing after Fabinho and Naby Keita.
Liverpool made a breakthrough in negotiations last night with Michael Edwards leading talks with Lyon president Juan Michael Aulas.
The wily Frenchman has been a tough negotiator and would have preferred to have waiting until after the World Cup for a deal.
But Liverpool have been determined to beat the clock and have Fekir signed up before France fly to Russia this weekend.
Liverpool will pay £48m rising to £53 and he will sign a five-year contract.
Liverpool have always been intent on getting the deal done before World Cup fever takes over, while Lyon were keen to see how he did incase his value rose.
But Fekir has been convinced to join Jurgen Klopp’s Liverpool revolution rather than wait on interest from Atletico Madrid and Bayern Munich to be firmed up.
Reports in France have claimed Klopp has personally convinced Fekir to pick Liverpool and he will sign a five-year deal at Anfield.