The clubs are yet to agree a fee, but talks could conclude on Friday about a deal that may amount to 60m euros - 55m plus a maximum of 5m add-ons.
The 24-year-old is expected to finalise his mega-money switch on Friday afternoon once he has completed a medical at Clairefontaine, the France national team's training base.
It had been reported that the Frenchman would complete his move to Anfield before the tournament kicks off in Russian Federation, but Lyon President Jean-Michel Aulas today (Thursday) said that it was far from a done deal. Liverpool, however, continued to press ahead with negotiations and appear to have broken Aulas's resolve to keep the attacking midfielder until after the World Cup in the hope of starting an auction.
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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. "The deal will certainly not be closed during the World Cup and I don't think there will be any change before the World Cup".
Fekir has also drawn interest from Chelsea and Bayern Munich, but Liverpool have been aggressive in chasing his signature.
Shaqiri, 26, has a release clause of just £12m after Stoke were relegated to the Championship.