The attacking midfielder has been heavily linked with Liverpool in the past few weeks, with reports in the French media prematurely declaring a £62 million agreement between Lyon and the Reds had been reached.
However, reports have continued to gather pace with the Reds' interest in the French international now being confirmed by local club journalists, including Liverpool Echo's James Pearce and The Times' Paul Joyce.
According to latest reports, the club will "step up the pursuit" of Fekir following Saturday's Champions League final against Real Madrid in Kiev, whilst they are confident they can swiftly reach an agreement for the 24-year-old.
Fekir is expected to make a £60 million transfer from Lyon, who he has played for since his youth days. Asked about the possibility of moving to Liverpool, the 24-year-old is quoted as saying: “Why not? Later there can be discussions with the president, with my entourage, to make a decision. In life, nothing can be forbidden.”
Liverpool will be eager to build on their success in the Champions League this season, with the club expected to be heavily involved in the transfer market this summer.
The midfielder, who was named as part of France's World Cup squad, is seen at Anfield as the ideal replacement for Philippe Coutinho - who joined Barcelona for £142 million in January - due to his abilities to play in the midfield three or in an advanced role, much like the former.
Lyon president Jean Michel Aulas said earlier this week that whilst there had been "no contact" from Liverpool, he warned that clubs “will have to be very, very rich to sign Fekir”.
This would be no issue for Liverpool, who are also set to pocket £70 million for reaching the Champions League final on Saturday.
Fekir, who was named Lyon captain last year, has had a sensational season in France, scoring 23 goals as he led his side to Champions League qualification.