The Reds signed Brazil global Fabinho in a £40m deal from Ligue 1 side AS Monaco last month.
France global Fekir was set to join the Reds for around £53m but the switch collapsed at the last minute due to medical concerns.
It is thought the club are still keen to bring in the midfielder and will be boosted by the statement made by Lyon manager Bruno Genesio in which he conceded that Fekir would be allowed to leave this summer if a "bigger club" wanted to sign him.
However, Aulas has now suggested the player wants to remain in France.
Lyon will compete in the Champions League next season after finishing third in Ligue 1 last season, largely down to the impressive performances of Nabil Fekir.
Nabil Fekir has since been in Russian Federation on worldwide duty representing France at this summer's World Cup, in which his nation have reached the quarter finals where they will face Uruguay.
"I have a near father-son relationship with my players, and I gave him the opportunity to join Liverpool due to their legendary status".
"I gave him the opportunity to go to Liverpool because it is a legendary club".
"I did that too with (Corentin) Tolisso and (Samuel) Umtiti, he is our captain and it is the coach's wish to keep him".
Jurgen Klopp's side have begun strengthening their squad this summer, having already signed Fabinho and Naby Keita in the central midfield places. 'I am happy, ' he told LFCTV. We will see after the World Cup.
I understand that the reason a deal for the 24-year-old collapsed was because Liverpool were unwilling to risk spending so much money on a potentially injury prone player.
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