The Reds star’s agent is due to meet with officials from the Italian club later this week, with the Serie A side eager to land the powerful defender.
Any move will come as a shock for Liverpool fans, with Sakho widely seen as the second best centre-back at Anfield behind Martin Skrtel.
Although the 25-year-old has endured a tough time at the club since his 2013 arrival, he has shown signs of promise and was particularly impressive when Brendan Rodgers switched to a three-man backline over the latter stages of 2014/15.
Sakho has also played a big role in the club’s recent pre-season games in the Far East and Australia, finding the back of the net with a powerful header against the Thailand All-Stars in Bangkok last week.
Lazio are eager to snap him up on an initial loan deal with a view to a permanent transfer next summer, and can offer the former Paris Saint-Germain man Champion League football.
The Rome giants have also been linked with unwanted Liverpool striker Fabio Borini.