The 26-year-old reportedly wants to leave the Premier League side.
The Black Cats appeared to be leading the charge for the 26-year-old having reportedly made an £11m bid, but the Express and Star suggests that the Baggies are considering making their own move.
While whether West Brom follow up their interest with a bid remains to be seen, it appears inevitable that Sakho will not be following the Hammers to the Olympic Stadium.
The Express and Star reports that the Senegal international has told Slaven Bilic that he wishes to leave the Irons this summer after becoming concerned about how many opportunities he will get next season following talk that the club are willing to spend around £30m on a new goalscorer.
With Salomon Rondon being the only member of Tony Pulis' squad to score more than four goals this past campaign, it is fair to say that they could surely do with extra depth up front.
Though Sakho has endured a mixed season - with just five goals coming in the Premier League - he has previously shown that he can enjoy ruthless runs of form, and that may be what tempts the Baggies into officially joining the race for his signature.