As it stands, Keita will complete a move to Anfield in the summer under a deal reached with the German side last year, but Liverpool are interested in signing Keita in January.
The sale of Philippe Coutinho to Barcelona has left a space in Jurgen Klopp's squad, and the Reds are looking at the possibility of paying extra money to bring in the 22-year-old before the end of the month.
However, according to the Liverpool Echo, the two clubs are yet to agree terms with RB Leipzig said to want the player to help them earn a place in the top four of the Bundesliga standings.
Since agreeing to sign for Liverpool, Keita has not continued his form at Leipzig, with just five goals and one assist coming from 20 appearances in all competitions this season.
On Friday, Klopp revealed that there had been 'no change' to the agreement between the two clubs.