If Sunderland are able to win they could leapfrog Norwich City in the Premier League table and move out of the bottom three.
However, a defeat would leave them in serious danger of going down, with time running out for the Wearsiders to save themselves.
Keown is not particularly confident with his prediction, but the former Arsenal defender does feel that Sam Allardyce’s men will just edge past West Brom.
“Tony Pulis doesn’t lose too many games on the bounce and after a disappointing home defeat to Norwich, he will demand an improvement,” Keown said.
“With West Brom safe I wonder whether Pulis will try to play more expansive football. If they do, that could play right into Sunderland’s hands. This is an absolute must-win game for Sam Allardyce but if West Brom open up, that could open the door for Sunderland.
“Home win, but I’m not saying that with much confidence.”
Sunderland have put in some excellent performances in recent weeks, but they have not accumulated points at a fast enough rate.
The Black Cats have been guilty of throwing away leads in the latter stages of matches, and that has stopped them climbing out of the relegation zone.
Sunderland are currently in 18th place in the Premier League table, two points adrift of safety.
West Brom, meanwhile, are well clear of the drop - but they will be looking to bounce back from defeat to Norwich City in their last fixture by picking up the three points at the weekend.