The Reds were reported to have made two bids to sign the Guinea international earlier this summer but the Bundesliga side rejected the offers.
According to speculation in the British media, Liverpool were weighing up a third bid possibly worth £72m to sign the 22-year-old box-to-box midfielder.
However, RB Leipzig manager Ralph Hasenhuttl ruled out the Africa star leaving the Bundesliga runners-up in the current transfer window.
Keita is thought to have a contract release clause worth £48m that can be activated next summer.
And the club’s sporting director Ralf Rangnick has conceded that he doesn’t expect Keita to sign a new contract in a possible boost to Liverpool’s hopes of signing the Guinea man next summer.
“I am not currently assuming that we will be able to extend his contract prematurely,” Rangnick told Sport Bild via Goal.
“I can assure you that Naby will be playing with us this season. All other scenarios also depend on how we do this season, how Naby plays himself and so on.”
Liverpool have signed three players in the summer transfer window so far as Jurgen Klopp looks to build his squad ahead of the new season.
The Reds have signed Mohamed Salah, Dominic Solanke and Andy Robertson ahead of their return to the Champions League.
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