Fabinho became Liverpool's first signing of the summer when he penned a long-term contract with the club yesterday evening, but the Reds are also thought to be interested in bringing in a new goalkeeper and Fekir before the start of the World Cup.
Lyon president Jean-Michel Aulas has suggested that there have been no talks with Liverpool over a deal for the France international, but Fabinho is eager to play alongside him at Anfield after facing him on numerous occasions in Ligue 1.
"He is a very good player, of international level. In Ligue 1, it is not only this season that he has demonstrated things. For a few years he has shown his quality. If he comes, it will be good too," the Brazilian told RMC Sport.
Fekir is expected to cost around £60m, which would take Liverpool's summer spending beyond the £150m mark following the agreed arrivals of Fabinho and Naby Keita.