Liverpool were close to landing Fekir from Lyon in June but, because of concerns about the player’s long-term history of knee problems, a transfer collapsed.
Since then, reports have claimed the Reds are still eyeing the 24-year-old.
However, the Liverpool Echo say Liverpool have decided NOT to reignite their interest in the World Cup winner.
The Reds have had a stellar summer so far, landing Naby Keita, Fabinho, Alisson Becker and Xherdan Shaqiri.
Liverpool were, however, initially in the market for a new No 10.
Philippe Coutinho jumped ship to Barcelona in January and, back then, the Merseyside club made the bold decision of not signing a replacement.
It was Fekir, though, who was eventually chosen.
But the Liverpool Echo say Lyon are confident the player will stay put despite the potential for a move elsewhere still being on the cards.
Some Liverpool fans were pining for Fekir earlier today when Klopp hinted at possibly making one more signing.
The Reds manager said: “We will see what happens.
“I cannot kill your D-day show, people sit there in front of the television all day waiting.
“If any player from my team is available, then in every other situation in my life as a manager I would have bought all of them, to be honest.
“They are all fantastic boys, they are able to play fantastic football.”
As well as Fekir, Liverpool have been linked with Besiktas powerhouse Domagoj Vida.
But the Reds believe their name is being used purely so the Turkish side can ramp up the player’s price for other suitors.