Blues are named in Group H alongside Derby County, Leeds United and Wolverhampton Wanderers.BCFC
The draw has taken place for this season's Premier League Cup.
The PL Cup is for English clubs' Under-23s sides and runs alongside the Professional Development League.
Blues are named in Group H alongside Derby County, Leeds United, Wolverhampton Wanderers.
There are eight groups of four, totalling 32 sides in the group stages.
Each team will play the other home and away, before the top two sides progress through to the knockout stages of the competition. Dates will be confirmed in due course.
The current holders of the trophy are Everton, who beat Newcastle United in last season's final.
The 2019/20 Groups are as follows:
Group A: Charlton Athletic, Colchester United, Reading, Swansea City
Group B: Everton, Fulham, Plymouth Argyle/Yeovil Town, Watford
Group C: Hull City, Newcastle United, Southend/Scunthorpe United, West Bromwich Albion
Group D: Aston Villa, Cambridge United/Exeter City, Doncaster Rovers, Portsmouth
Group E: AFC Bournemouth, Nottingham Forest, Southampton, Stoke City
Group F: Huddersfield Town/Oxford United, Liverpool, Sunderland, Wigan Athletic
Group G: Blackburn Rovers, Burnley, Crystal Palace, Middlesbrough
Group H: Birmingham City, Derby County, Leeds United, Wolverhampton Wanderers
There are four qualifying matches that will determine the final line-up of the groups, with the fixtures below to be played prior to the beginning of the group stages.
Monday 9 September: Huddersfield Town v Oxford United
Tuesday 10 September: Cambridge United v Exeter City, Southend v Scunthorpe United
Thursday 12 September: Plymouth Argyle v Yeovil Town