Strong speculation had linked Fekir with a move to Merseyside as a replacement for Philippe Coutinho.
However, he has since come out to put to bed the rumours, arguing that he is in no rush to decide his future.
Fekir also revealed that talks had begun with several clubs but that Lyon president Jean-Michel Aulas backed his decision either way.
He said: "I'm not close to Liverpool. It's true that there are discussions with several clubs. As I said, I will take the time to think.
"It does not matter if I sign or not before the World Cup. As I said, I leave time to do things.
"[Aulas] knows my desires, and we'll talk about all of this in the next few days."
The comments will come as a slight blow for Liverpool, who are still linking their wounds following a disappointing 3-1 defeat to Real Madrid in the Champions League final on Saturday.