According to the British tabloid, the Reds have identified the 24-year-old as the ideal replacement for the recently departed Philippe Coutinho, with a potential £60 million deal being mooted.
Jurgen Klopp laughed off the speculation when quizzed about it in his post-match press conference following his side's 1-0 defeat to Chelsea, but Mane believes that the France worldwide would be a very good signing for the club.
Klopp's Reds are currently flirting with danger regarding a Champions League spot and now must win their last game in order to qualify for Europe's elite.
Either way, signing Fekir would see the Reds add more goals to their midfield, with the 24-year-old scoring 22 this season, assisting a further 7.
Klopp's comments came after Lyon owner Jean-Michel Aulas denied that Fekir was set to move to Anfield. I am a bit surprised by this story.
Fekir is reported to have agreed a five-year deal, and that he was in England a number of weeks ago to finalise the deal.
"But no comment. What was the second name?" Now I am interested!
Liverpool have though already agreed a deal to sign Naby Keita at the start of July, but were always likely to sign more players to build upon their stunning Champions League form and challenge at the Premier League title.
"I also want to say there was no agreement in Nabil's contract allowing him to leave".
"We have had no contact with Liverpool today", he said.
"Nabil is a very great player, if that's the case, we will be really happy to have him here", he said when told of the rumours.