According to German outlet Bild (via Ian Doyle in the Liverpool Echo), the German outfit are prepared to let the midfielder leave in the current transfer window if the Reds pay a premium of between €15 million and €20 million (£13 million and £17.5 million).
Previous reports suggested Leipzig were resistant to the idea of losing one of their best players six months before they initially planned, but the club now need to raise funds to comply with UEFA's financial fair play rules, per Doyle's report.
However, RB Leipzig manager Ralph Hasenhuttl said Keita will not leave in January, adding that "nothing has changed" and the club have no reason to sell, via Kaveh Solhekol of Sky Sports.
Last summer Liverpool agreed a deal worth over £50 million to sign Keita in July 2018.
The recent departure of Philippe Coutinho to Barcelona for £142 million has left the Reds lacking in star quality in the midfield, but their initial plans to persuade Leipzig to let Keita leave early looked to be in vain, per football writer Chris Williams:
Per Williams, though, the move is now a genuine possibility as Keita himself is keen for it to happen:
Chris Williams @Chris78Williams
Further to reports in Bild and Kicker: Leipzig would consider allowing Keita to leave in Jan should a fee be agreed up on that suits both #RBL & #LFC. Leipzig are holding out for the highest possible return. Crucially Keita has now expressed a desire to leave during this window.
The arrival of the 22-year-old box-to-box star would be a big boost for Liverpool, especially after the disappointment of losing Coutinho, who has been the Reds' key player for the last three seasons.
Keita would not be a direct replacement for Coutinho. However, along with his defensive capabilities, the Guinea international is also comfortable on the ball and can be a huge asset going forward, per WhoScored.com:
He is one of the most complete midfielders in Europe and has the potential to become a talismanic presence at Anfield.
Jurgen Klopp's squad is lacking in the engine room, but Keita could be the solution to that problem and could work effectively in a 4-3-3 or 4-2-3-1 system at Liverpool.
His arrival in January would be a boon for the Reds, and it is looking an increasingly likely possibility.