The 23-year-old France international has not played a single minute this season and has fallen behind Brazilians Thiago Silva and Alex who are coach Laurent Blanc's favoured pairing.
French broadcaster beIN Sport, whose chairman Nasser al Khelaifi is also chairman at PSG, reported on Friday that the French champions had agreed to sell Sakho to Liverpool for 23 million euros ($30.33 million).
Media reports have also linked him with a move to AC Milan.
Sakho, who has 14 international caps, asked to leave the club after France coach Didier Deschamps left him out of this month's friendly in Belgium because of his lack of competitive action.
The powerful centre back, who was part of the PSG academy, has played 151 league games for the club and was named Ligue 1's young player of the year by his peers in 2011. ($1 = 0.7584 euros)
(Reporting by Gregory Blachier; Editing by Toby Davis)
