The proposed deal was first reported by beIN Sport – a TV channel that is owned by Qatari Sports Investments, the same group that owns Paris Saint-Germain.
Sakho, 23, has spent his entire career at PSG but his place in the side has come under pressure since the £27m summer signing of Brazilian teenager Marquinhos from Italian side Roma.
According to Maxime Dupuis of Eurosport France the beIN Sport report should be taken "very seriously" and he has backed Sakho to be a success in the Premier League.
"He is not as technically gifted as some defenders but he is really, really tough," said Dupuis. "He's a beast and some forwards have admitted to being afraid of him in the past.
"Sometimes he makes mistakes but he's young. I think he could have a good future at Liverpool.
"The fee might seem a little bit high but he's a real player. Physically, he is very impressive."
Sakho was born and raised in Paris and has won 14 caps for the French national team.
Meanwhile, according to other reports Liverpool are looking to sign Sporting Lisbon defender Tiago Ilori and that the player might already be on his way to Anfield for a medical.
The 20-year-old would cost around €8.2m (£7m).
It is unclear whether Liverpool are interested in signing both players or just one of them.