A story from RMC Sport in France claimed on Sunday the Reds had concluded a deal for the 23-year-old attacking midfielder.
Lyon owner Jean-Michel Aulas has today, though, denied that Fekir is on his way to Anfield.
"I think he would do very good things with us".
"We always need this kind of player, if we have him it'll be fire".
As well as Fekir, Liverpool have also been linked with a stunning move for Barcelona's Ousmane Dembele who only arrived in Catalunya last summer.
Afghanistan: 12 killed in blast inside mosque in Khost
Television reports said local police officials had been told by the Taliban that the Indians were being held by the group. They were abducted while traveling to the area, where the company owns an electricity sub-station contract.
Reports in France continue to suggest that Liverpool are in pole position to secure the talented attackers signature, although Arsenal and Chelsea are also said to hold an interest in the player.
"I'm from Liverpool, I never comment on the rumours, already I said much more than I usually say".
Aulas also dismissed the speculation following a 3-0 Ligue 1 win over Troyes that saw Bruno Genesio's second-place side bolster their hopes of automatic qualification for next season's Champions League group stage. Fekir is here, ' he said.
Fekir admitted that Lyon qualifying for the Champions League could be enough to keep him at the club beyond the summer.
Although Mariano Diaz and Memphis Depay have both enjoyed fine seasons, Fekir is the man at the hub of Lyon's sparkling attacking play.
The Ivory Coast global is understood to be desperate to play European football next season, and will look to end his second spell with his boyhood club in the pursuit of furthering his career with a Premier League giant. I am still in Lyon.