He has won a place in the France World Cup squad for his performances, though Antoine Griezmann is set to be preferred to him in the starting XI for Saturday's final warm-up friendly against the USA.
However, it would appear Lyon president Jean-Michel Aulas is likely to sell Fekir after the World Cup.
"Olympique Lyonnais is delighted to be able to count on the presence of their captain in 2018-2019", Lyon said in a statement.
Parker looking forward to 'war' with Whyte
It is a fight which has seemingly come out of the blue, with American Bryant Jennings initially the favourite to be Parker's next opponent.
A product of Lyon's successful youth academy, the skillful forward has 58 goals in 161 games for Lyon.
The French worldwide, who is now with France national team ahead of the World Cup in Russian Federation, has been heavily linked with the Merseyside club, with reports suggesting a deal had been struck earlier this week.
The 24-year-old was being courted by Liverpool as a replacement for Philippe Coutinho, who joined Barcelona in January.
Speculation is swirling about why the deal has not been rubber-stamped.
However a statement from Les Gones on Friday, suggesting that media reports claiming a deal had been reached were false, cast doubt on a positive outcome for the Merseysiders.