The France international had been identified as a potential long-term replacement for Philippe Coutinho and was close to completing a move to Anfield this summer.
Fekir travelled to Merseyside in June after a fee had been agreed with Lyon, and even reportedly conducted an interview with LFC TV.
However, the Premier League side sensationally pulled the plug on the deal at the 11th hour, leaving Fekir struggling to come to terms with his future.
The 25-year-old, though, has now put the disappointment of the failed transfer behind him and insists he just wants to move on.
Speaking to reporters after Lyon's 2-0 Ligue 1 victory against Strasbourg on Friday, Fekir said:
Yes, the missed transfer to Liverpool is totally digested. These are things that happen. It's like that. We must advance. It's ancient history.
I heard several things. The real reason is that they [Liverpool] only know it.
My future? I am Lyonnais and I will stay. For the extension, we'll see! Why not? I am in Lyon, I am good.
It is true that things happened this summer, but there is a new season starting in Lyon and I am very happy to be here.