The Sun reports that the Albion attempted to sign the 26-year-old in the summer, and that Pulis remains an admirer of the France international who has fallen well out of favour at Anfield under Jurgen Klopp.
However, West Brom are now unlikely to follow up their interest with another bid during the upcoming window, according to The Sun, as Pulis now wants to bolster his midfield and striker options.
West Brom manager Tony Pulis
They have conceded just 16 times in the league this term, and as Sakho has not played any first-team football since the Merseyside derby victory over Everton last season, it could be argued that he may not add that much if he was brought in.
The news that West Brom are not planning to make a move will undoubtedly prove a blow to Sakho's chances of becoming a key man at a club side in England. As mentioned, his days at the Reds appear numbered given his lack of game-time, and The Sun suggests that Inter Milan are now favourites to sign him.