The Reds activated Keita's £48m ($62m) release clause which comes into force only this summer by agreeing to pay a premium and concluded a deal for the midfielder. He is expected to arrive at the end of the current campaign for a reported fee of £57m and is said to have agreed to a five-year deal with the Anfield outfit.
However, Philippe Coutinho's transfer to Barcelona earlier this month has changed Liverpool's stance and they are keen to bring forward the deal and get Kieta to Merseyside during the ongoing January transfer window. Red Bull Leipzig are not keen on allowing a key player to leave midway through the campaign and have thus far stood firm.
Jurgen Klopp is keen to fill the void in his midfield following the Brazil international's departure and is said to believe Keita can provide the necessary cover. The Guinea international will be unable to play in the Champions League but will give added squad depth in the Premier League as Liverpool battle for a place in the top four.
According to German publication Bild, Leipzig bosses were initially against the transfer during the winter transfer window, but are said to have softened their stance in recent weeks. The report claims that Liverpool will be allowed to sign Keita this month if they agree to pay the Bundesliga club an added €15 to €20m, which will allow them to find a replacement for the midfielder.
The German club is not short of funds owing to energy drinks company Red Bull's backing, but are said to want to raise funds to invest to keep with Uefa's Financial Fair Play regulations. It remains to be seen if the Reds are willing to pay an added fee as they are already paying a premium to sign him in the summer.
Liverpool have also been linked with Thomas Lemar and Riyad Mahrez in recent weeks as replacements for Coutinho. But even the AS Monaco midfielder and the Leicester City star are valued at £60m and £50m respectively.