Manchester United will face League Two side Grimsby Town in the second round of the Carabao Cup, plus there are two all-Premier League ties.
Bournemouth will host Brentford while Wolves will play West Ham when the 11 Premier League clubs not participating in a European competition enter the Carabao Cup in the second round.
The draw took place live on Sky Sports, shortly before Championship duo Birmingham and Sheffield United faced off in the first round of the competition at St Andrews Stadium.
The winner of that tie will host Port Vale.
The EFL confirmed Premier League teams that had qualified for Europe last season would receive an automatic bye into round three.
Liverpool, Manchester City, Arsenal, Chelsea, Tottenham, Newcastle, Aston Villa, Nottingham Forest and Crystal Palace are the nine top-flight clubs who have automatically progressed.
Carabao Cup second-round ties will be played during the week commencing August 25.
Carabao Cup second round in full:
Grimsby vs Man Utd
Fulham vs Bristol City
Norwich vs Southampton
Oxford United vs Brighton
Reading vs AFC Wimbledon
Bournemouth vs Brentford
Millwall vs Coventry
Wolves vs West Ham
Swansea vs Plymouth
Bromley vs Wycombe
Cardiff vs Cheltenham or Exeter
Cambridge Utd vs Charlton
Tranmere or Burton* vs Lincoln
Accrington vs Doncaster
Wigan vs Stockport
Stoke vs Bradford
Burnley vs Derby
Sunderland vs Huddersfield or Leicester
Birmingham or Sheffield Utd vs Port Vale
Preston vs Wrexham
Barnsley or Fleetwood vs Rotherham
Bolton or Sheffield Wednesday vs Leeds
Everton vs Mansfield
*Tranmere vs Burton was postponed and will be played on Tuesday, August 19.
