The Reds confirmed past year that they had successfully agreed a £48m deal to sign Keita on July 1, 2018, but the recent sale of Philippe Coutinho has forced the Reds to attempt to bring the transfer forward.
A £51million deal is already in place for the Guinea worldwide to arrive in the summer.
The report suggests that Leipzig may need to raise funds in order to comply with UEFA's Financial Fair Play rules and would be open to an early move if Liverpool pay between £13m- £17.5m.
"The situation is the same as it was all season - there's no reason for us to let Naby Keita go early", he told the BBC.
Philippe Coutinho's exit means Liverpool have lost their most creative midfielder; the Brazilian set up 40 goalscoring chances in the league this season, five more than any teammate, and also managed the most assists (6).
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Liverpool reached an agreement with RB Leipzig last summer for the Guinean midfielder to transfer to the English team next summer in exchange for €75 million ($91.5 million).
European's elite competition could be a vital factor in any possible deal though as RB Leipzig are fighting for qualification into the Champions League and may want to hold on to such a player.