However, Fekir insists that he is "not close" to making a decision over his future and suggested that any move may have to wait until after this summer's World Cup in Russia.
"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," he told Telefoot.
"It does not matter if I sign or not before the World Cup. As I said, I leave time to do things. [Lyon president Jean-Michel Aulas] knows my desires, and we'll talk about all of this in the next few days."
Fekir has scored 23 goals in 40 appearances across all competitions for Lyon this season.