Albion have been drawn at home in the fourth round of the Emirates FA Cup.
They will take on either Liverpool or Wolverhampton Wanderers, having got through with a 5-1 win at Middlesbrough on Saturday.
Liverpool drew 2-2 with Wolves at Anfield and will replay at Molineux next week.
The tie will take place over the weekend of January 27-30 and more information together with ticket details will be confirmed soon.