The Guinean midfielder has been a key performer for RB Leipzig since joining a year and a half ago, but the 22-year-old will soon be at Anfield.
Until now it had appeared unlikely that Liverpool would be able to secure an earlier arrival, but matters have turned around somewhat.
German outlet Bild report report that RB Leipzig have had a change of heart and are now willing to discuss the move during the winter window.
Liverpool have already agreed a £55 million transfer, but an additional premium will be required to bring him in this month.
The report suggests €15-20m (around £13-£17.5m) will be needed to sway the Bundesliga team to release Keita early.
Crucially, the player himself has expressed a desire to depart and is now seen as having his head at Anfield, taking English lessons over German and “considered isolated” in the squad.
Leipzig must also generate revenue to meet Financial Fair Play rules, and Champions League qualification for next season is far from certain.
RB Leipzig were knocked out in the group stage of this season’s Champions League, so Keita wouldn’t be able to feature for the Reds in Europe—but he could play a key role in the league to ensure participation once more in 2018/19.