There are two all-Premier League ties as Fulham welcome Tottenham Hotspur and Nottingham Forest host Burnley in the Carabao Cup.
Gillingham's reward for knocking out Championship side Southampton in one of the shocks of the first round is a trip to recently-promoted Luton Town.
Two other top-flight teams also face fourth-tier opposition as Everton visit Doncaster and Newport host Brentford.
The second-round ties of the Carabao Cup will take place in the week commencing 28 August.
The eight Premier League sides to have qualified for Europe this season will join the competition in round three.
Northern section of The Carabao Cup:
Tranmere Rovers v Leicester City
Salford City v Leeds United
Harrogate Town v Blackburn Rovers
Stoke City v Rotherham United
Wrexham v Bradford City
Doncaster Rovers v Everton
Bolton Wanderers v Middlesbrough
Port Vale v Crewe Alexandra
Nottingham Forest v Burnley
Sheffield Wednesday v Mansfield Town
Wolverhampton Wanderers v Blackpool
Sheffield United v Lincoln City
Southern section:
Bristol City v Queens Park Rangers or Norwich City
Plymouth Argyle v Crystal Palace
Reading v Ipswich Town
Portsmouth v Peterborough United
Luton Town v Gillingham
Swansea City v Bournemouth
Fulham v Tottenham Hotspur
Exeter City v Stevenage
Wycombe Wanderers v Sutton United
Birmingham City v Cardiff City
Newport County v Brentford
Chelsea v AFC Wimbledon