Clarke's side will host former club Liverpool in Capital One CupALBION have been drawn at home to holders Liverpool in the Capital One Cup third round.
The tie will be played during the week commencing September 24.
The Baggies secured their place in the final 32 by winning 4-2 at League One leaders Yeovil on Tuesday.
Head coach Steve Clarke won the tournament with Liverpool last term in his previous role as first-team coach to Kenny Dalglish and masterminded a 3-0 victory over the Reds in his first game in charge of the Baggies 12 days ago.
This will be the sixth meeting in the competition between the two clubs and the first for 15 years.
Albion suffered a third-round exit against Liverpool in 1972/73 when, after drawing 1-1 at The Hawthorns, they lost the replay 2-1 at Anfield.
The Baggies gained revenge in the second round four years later when they drew 1-1 on Merseyside before edging the rematch 1-0 at The Hawthorns.
Liverpool won the last League Cup tie between the two teams 2-0 in the Black Country in October 1997.