Albion are believed to have offered to take the Frenchman on a season-long loan during the summer and were given encouragement by the Reds after their boss Jurgen Klopp decided he no longer featured in his plans.
However, Sakho rejected the opportunity to move to the Hawthorns, believing he could force his way back into Klopp's first-team squad.
Having failed to change the German's mind, rumours once again began to circulate that West Brom would try to take Sakho on loan for the second half of the season.
But the latest speculation suggests Tony Pulis has now ended his interest in the 26-year-old as he feels other areas of the team need reinforcing, rather than the defence, with a new midfielder and striker top of his January wish-list.
Sakho now looks set to leave the Premier League altogether with Italian duo AC and Inter Milan reportedly keen on his signature.