The France international has become a top target for Jurgen Klopp's side, and Goal understands the Merseyside club are hopeful of wrapping up his transfer before he leaves for the 2018 World Cup.
However, Lyon president Jean-Michel Aulas insisted earlier this week that the attacking midfielder's future will not be decided until after the summer tournament, and the French club have taken to dismissing reports that a move is in the closing stages.
"The information about the transfer of Nabil Fekir is false," the club tweeted on Friday. "Olympique Lyonnais categorically denies the false information disseminated by media about the transfer of Nabil Fekir to Liverpool."
"In this period of transfers where the slightest rumour is often presented as a reality, Olympique Lyonnais recalls that only the information released by the club on its website is authentic."
The 24-year-old is said to be keen on a move to Anfield, but the French club are hoping positive displays in Russia could see demand and his asking price increase before he is sold.
Liverpool have been active in the transfer market already. The Reds will see Naby Keita join from RB Leipzig after agreeing a deal last year, while Fabinho arrived from Monaco this summer and urged Fekir to join him at Anfield.
"He is a very good player, of international level. In Ligue 1, it is not only this season that he has shown things," Fabinho said.
"It's been a few years of him demonstrating his quality. If he comes, it will be good too."
Fekir, who scored 23 times in 40 games as Lyon finished third in Ligue 1, is contracted to the club until 2020.