Albion have been handed another home draw in the Carabao Cup.
They will host holders Liverpool in the fourth round in the week commencing October 28.
The game comes just a few days before the teams meet at Anfield in the Premier League.
Liverpool came through 5-1 against West Ham at Anfield his evening.
Albion have so far won at home to Crawley and Wolves this term but have only once reached the quarter-finals of the League Cup, way back in 1978-79.
Elsewhere, Manchester City will travel to Tottenham while Manchester United are at home against Leicester.
Championship outfit Preston’s reward for seeing off top-flight Fulham in an epic penalty shoot-out last week is a home game with Arsenal.
Sheffield Wednesday and Stoke go to Brentford and Southampton respectively.
There is another all-Premier League tie as Aston Villa host Crystal Palace, and a potential one if Newcastle get past League Two AFC Wimbledon, with the winners of that game to face Chelsea at home.
The AFC Wimbledon-Newcastle contest was due to be played at the Cherry Red Records Stadium on Tuesday night but was switched to St James’ Park next Tuesday after the former was affected by flooding.
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