A France international considered to be worth around £60 million ($81m) in the summer transfer market has seen his stock rise throughout a productive 2017-18 campaign.
It is now being suggested that Fekir could be the latest to drop off the production line of talent in Lyon and onto the books of a European heavyweight.
Liverpool are reported to be leading the chase for a much sought-after signature, but Lyon have no intention of selling and their president maintains that he has received no formal offers.
"I know that Nabil, now that we have qualified for the Champions’ League, would really like to stay, so we will discuss things calmly.
"He has magnificently won the right to go to Russia with France, which gives him an even higher standing.
"For the moment, nothing is done.
"You will have to be very, very rich to sign Nabil Fekir this year."
Fekir has offered no indication that he will be looking to force the issue when the summer transfer window opens.
The 24-year-old is a product of Lyon’s famed academy system and will do nothing to disrupt his home-town club, although he has not committed his future to them either.
Pressed on whether he had taken in his last game for the club following a 3-2 victory over Nice on Saturday, Fekir said: "Farewell? Frankly, I don't know.
"I spent an exceptional season here with players, fans and the staff. We ended up in beauty.
"You have to pass a course, it is true. I think I gave everything to Lyon.
"Now it is time to look into the future."