The 27-year-old has not featured for the Reds in their 4-0 win over Everton at Anfield in April 2016. The Merseyside club's manager Jurgen Klopp decided against including the central defender in his plans for the last season.
Sakho completed a loan switch to Crystal Palace earlier in January and he impressed for the Eagles. He was left out of Liverpool's pre-season squad and the former Borussia Dortmund was coy when asked about the centre-back's future at Anfield.
According to the Liverpool Echo, Klopp is open to the idea of sanctioning the France international's sale. It is believed that West Brom have identified Sakho as a transfer target. Tony Pulis identifies Sakho as the player to strengthen his side's defence.
Liverpool have slapped a £30m ($38.5m) asking price for Sakho, who is currently recovering from the knee injury he suffered in April while in action for Palace. The Baggies are not the only club interested in signing the player.
Sakho is open to the idea of returning to Selhurt Park, while Southampton and Napoli have also maintained their interest in landing the former Paris Saint-Germain man. He has already rejected an opportunity to join West Brom on loan last summer.
However, the Echo report claims that has not deterred Pulis from making an approach for him this summer. West Brom are looking for a possible replacement for Jonny Evans, who is attracting interest from Manchester City.
Pulis has admitted that his side will only sanction Evans' sale if City are ready to put an "enormous amount" of money in signing the defender. The Guardian claims a bid in the region of £25m ($32m) plus add-ons will consider West Brom to consider his sale.
Sakho's move to West Brom is likely to allow Evans to make a switch to the Etihad. Should the latter join City, he is likely to become City's eighth signing of the summer transfer window.
Guardiola's side have already completed deals for Bernardo Silva, Ederson, Kyle Walker, Douglas Luiz, Danilo, Benjamin Mendy and Olarenwaju Kayode.