Tony Pulis' men are 18th in the Premier League but Keith Downing's side, who secured their first win in 10 games on Wednesday, are four points ahead of the Eagles
The Baggies snapped a dismal run of form with a 1-0 Premier League victory over a 10-man Newcastle United on Wednesday.
Caretaker boss Keith Downing is still in charge and saw Saido Berahino score the winner, converting from the penalty spot four minutes from time.
After finishing eighth last term, West Brom sit 14th in the Premier League – just four points above the relegation zone – and will hope the cup provides a welcome distraction from their troubles.
Striker Shane Long could make his return from a calf injury, after he was an unused substitute against Newcastle.
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West Brom have not made it past the fourth round since 2010, when they reached the fifth, while they made the semi-finals in 2008 before losing to eventual winners Portsmouth.
They have won the FA Cup on five occasions, but not since 1968.
Palace came from behind to win a point in a 1-1 draw against Norwich City on Wednesday, but they remain in the Premier League's bottom three.
Jason Puncheon scored Palace's equaliser – also from the penalty spot – as they continued their strong home record under new manager Tony Pulis.
Pulis has seen his side win two and draw one of their four matches at Selhurst Park under his tutelage and continuing that form will be crucial in their bid for Premier League survival.
Midfielder Kagisho Dikgacoi entered the Norwich fixture under an injury cloud, and his hamstring problem flared up again, forcing him to be substituted.
He is now set to miss Palace's trip to West Brom, with Stuart O'Keefe (thigh) also in doubt.
Remaining on Palace's injury list are defenders Paddy McCarthy (groin) and Jack Hunt (ankle), midfielders Jerome Thomas (calf) and Adlene Guedioura (ribs) and striker Glenn Murray (knee).
Palace have been bundled out of the FA Cup in the third round in each of the last three years, with their best ever result coming in 1990 when they reached the final before losing a replay to Manchester United.
West Brom and Palace have played each other regularly in recent years, but never in the FA Cup.
Their most recent meeting was in November as West Brom notched their last win of 2013, as goals from Berahino and Gareth McAuley saw them triumph 2-0.