French outlet L'Equipe claim a medical will be undertaken by Friday, with Melissa Reddy saying that the deal is expected to be confirmed on Friday.
Nabil Fekir is to undergo a medical with Liverpool on Friday after the Reds thrashed out a fee with Lyon for his services.
But Lyon President Jean-Michel Aulas earlier said the deal would NOT go through until after the World Cup.
Despite this, Goal understands Liverpool believe a deal can be thrashed out before Fekir flies to Russian Federation with his national team this weekend.
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The 24-year-old attacking midfielder has been identified by Jurgen Klopp as Philippe Coutinho's natural replacement.
"The record is at a standstill, there is no way forward", said Jean-Michel Aulas.
Klopp and co. hope to complete the transfer before the commencement of the FIFA World Cup, next week. "(We) have not set a base price because we have not discussed this yet". Fekir is set to play for France on Saturday evening against the United States of America, a game that will take place in Lyon's Stade des Lumieres. They have also registered interest in Xherdan Shaqiri, who is available for £12m-£13.5m after Stoke City's relegation from the Premier League.