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.
Fekir provided 12 goals and nine assists in 39 games for Lyon, who secured a third-placed finish in Ligue 1 a year ago.
Rangers would love to take him back to Ibrox, but are unlikely to match Liverpool's asking price, while newly-promoted Aston Villa are among the clubs to have registered an interest in a permanent deal.
Liverpool will demand £12 million ($15.3m) for Ryan Kent this summer, with the young winger set to turn down the chance to join Leeds United on loan.More news: Death Comes Again as Russian Doll Gets a Season 2
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Speaking in the days after the breakdown of his initial move to Anfield, the player's agent claimed that it was "not the end of the story", while last month Lyon president Jean-Michel Aulas confirmed he will leave this summer.
But Liverpool are not prepared to offer as much money as they put on the table a year ago.
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.
But it is believed that the European Champions have no intention of paying anywhere near the fee that was agreed with Lyon last June.
Lyon-based newspaper Le Progres claim the upcoming friendly between Lyon and Liverpool in the Swiss capital of Geneva on July 31 could play a part in negotiations.