Keita was reported to have undergone a medical at Liverpool's Melwood training base.
Several news outlets, including the BBC and the Times, said Liverpool have agreed to pay a £48 million ($62 million, 51.9 million euros) release clause to sign the 22-year-old.
They will reportedly pay an undisclosed premium as well.
Keita was reported to have undergone a medical at Liverpool's Melwood training base on Monday. He will officially join the club on July 1, 2018.
Liverpool's previous transfer record was the £35 million they paid Newcastle United to sign Andy Carroll in January 2011.
An athletic box-to-box midfielder, Keita has been a longstanding target for Liverpool manager Jurgen Klopp.
He began his career with Horoya in his home city of Conakry and spent a season at French second-tier side Istres before joining Red Bull Salzburg in 2014.
Salzburg sold him to their German sister club RB Leipzig in June last year.
Klopp has signed Egyptian winger Mohamed Salah, Scottish left-back Andy Robertson and English striker Dominic Solanke during the current transfer window.
Liverpool's 4-0 win over Arsenal on Sunday left them second in the Premier League table, two points below Manchester United.