But Lyon President Jean-Michel Aulas earlier said the deal would NOT go through until after the World Cup.
"The transfer will certainly not close during the World Cup and I do not think there is any change before the World Cup", Aulas claimed.
"We haven't set a starting price because we haven't discussed that yet".
Les Bleus will take on the United States this weekend, in their final World Cup tune-up.
The Independent report that Aulas believes that Liverpool will have to calculate the potential of summer performance into their offer.
Bayern Munich and Atletico Madrid are also reportedly interested in the French global - but Liverpool are now in the driving seat. They have also registered interest in Xherdan Shaqiri, who is available for £12m-£13.5m after Stoke City's relegation from the Premier League.