A year ago the Reds were on the verge of completing a £53million transfer - to the extent that the player had been interviewed for club media and been photographed in a shirt - when they pulled out over concerns about a historic knee injury.
Liverpool sought a second opinion after the initial medical and decided not to risk proceeding with such a high-value transfer.
Reports in France claim they are still interested in the 25-year-old, who is entering the final 12 months of his contract, and there was even a suggestion a five-year contract had been offered.
But Press Association Sport understands the club's stance has not changed since the player failed his medical and the deal was declared dead.
Lyon president Jean-Michel Aulas has admitted there is "an understanding" to allow Fekir to leave.
However, with the club still wanting around £45million for a player with just 12 months left on his contract it would benefit the Ligue 1 club if they can generate an auction for his services.
Meanwhile, Liverpool are considering scrapping their Anfield friendly with Schalke as it is just three days before their Friday-night Premier League season-opener at home to Norwich.
Jurgen Klopp's side have pre-season games at Tranmere and Bradford ahead of a trip to America for matches against Borussia Dortmund, Sevilla and Sporting, before returning to face Napoli at Murrayfield and Fekir's side Lyon in Geneva on July 31.
Schalke, managed by former Huddersfield boss David Wagner, were due to be the visitors for the only summer friendly at Anfield on June 6 but that has now been thrown into doubt.
A message on the ticket section of Liverpool's website for the game in question stated "Ticket sales for this fixture have been postponed."
