Keita, a Guinea international, will move to Anfield on July 1 after the Reds struck an agreement with the Bundesliga club last summer.
According to the Liverpool Echo, the Merseyside club's deal included an agreement that the final price paid would depend on Leipzig's finishing position this season.
The report claims that Champions League qualification was set to guarantee a £59m fee, Europa League qualification amounted to £52.75m, and no European football would have cost Liverpool £48m.
Leipzig finished sixth in the Bundesliga table this term, securing a Europa League spot, which means that the Reds will have to shell out £52.75m.
Keita has made 39 appearances this season, scoring nine goals and registering seven assists.