Paris Saint-Germain accept the Premier League side's offer, with the Reds also closing in on Sporting Lisbon defender Tiago Ilori as they look to bolster their defensive options
The Reds will pay the Ligue 1 champions a 17 million euro ee for the 23-year-old defender as Brendan Rodgers looks to improve his defensive options for the 2013-14 campaign.
Sakho has played over 150 league games for PSG, with the Frenchman having been capped 14 times by his country, and he will compete with Daniel Agger and Kolo Toure for a place in Rodgers's starting XI.
Liverpool is also close to agreeing a deal for Sporting Lisbon youngster Tiago Ilori, with the Reds having tabled a €7m offer plus performance related bonuses to sign the 20-year-old.
Rodgers has felt the need to dip into the market for defensive reinforcements with the future of Martin Skrtel remaining up in the air, with Napoli strongly linked with a move for the Slovakia international.
The Anfield manager's options have been further limited with Sebastian Coates sidelined with a long-term knee injury, while Andre Wisdom's patchy preseason performances have done little to convince Rodgers that he is ready for a regular first-team berth.
There is better news regarding Kolo Toure's fitness, however, with Rodgers revealing on Friday that the Ivorian could recover from a groin problem in time to face Manchester United on Sunday.