The 2023 winners will head for Blundell Park during the week beginning August 25 after being paired with the Mariners in Wednesday night's draw, in which they were the last team team out of the hat.
Elsewhere, there are all-Premier League clashes between Bournemouth and Brentford and Wolves and West Ham, while promoted Leeds face a trip to either Bolton or Sheffield Wednesday and Everton will host League One Mansfield.
League One Doncaster's reward for their 4-0 drubbing of Championship club Middlesbrough is a trip to Accrington, while Bromley host League One Wycombe after dumping Ipswich, who spent last season in the Premier League, out on penalties.
The nine top-flight sides involved in Europe this season - Liverpool, Arsenal, Manchester City, Chelsea, holders Newcastle, Tottenham, Aston Villa, Nottingham Forest and Crystal Palace - will enter the competition in the third round.
Draw
South Section
Fulham v Bristol City
Norwich v Southampton
Oxford v Brighton
Reading v AFC Wimbledon
Bournemouth v Brentford
Millwall v Coventry
Wolves v West Ham
Swansea v Plymouth
Bromley v Wycombe
Cardiff v Cheltenham or Exeter
Cambridge v Charlton
North Section
Tranmere or Burton v Lincoln
Accrington v Doncaster
Wigan v Stockport
Stoke v Bradford
Burnley v Derby
Sunderland v Huddersfield or Leicester
Birmingham or Sheffield United v Port Vale
Preston v Wrexham
Barnsley or Fleetwood v Rotherham
Bolton or Sheffield Wednesday v Leeds
Everton v Mansfield
Grimsby v Manchester United
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