Fabinho's switch to Anfield from Monaco was confirmed on Monday, the Brazil international signing a long-term contract after the clubs agreed to a deal worth €45 million (£39m/$52m) plus bonuses of up to another €5m.
Asked if he wanted Fekir to sign for Liverpool, Fabinho told RMC Sport: "Yes.
"He is a very good player, of international level. In Ligue 1, it is not only this season that he has shown things.
"It's been a few years of him demonstrating his quality. If he comes, it will be good too."
Fabinho joined Liverpool after five seasons at Monaco, where he won the Ligue 1 title in 2016-17.
After scoring in France's 2-0 friendly win over the Republic of Ireland, Fekir said: "If Fabinho will be my future team-mate? I will discuss about my future after the World Cup, not before.
"If I will sign somewhere before the World Cup? Honestly, I don't know."