Manchester City have won the Carabao Cup eight times, last lifting the trophy in 2021
Holders Manchester United will face Crystal Palace at Old Trafford.
Aston Villa host Everton, Brentford play Arsenal and Brighton travel to Chelsea in the other all-Premier League ties.
League One side Lincoln's reward for beating Sheffield United on penalties is a home tie with West Ham, while Salford City host Burnley.
Fulham, who beat Tottenham on penalties in the second round, host Championship side Norwich, while nine-time winners Liverpool are at home to Leicester.
The third-round ties will take place in the week commencing 25 September.
Ipswich Town v Wolves
Exeter City v Luton Town
Aston Villa v Everton
Manchester United v Crystal Palace
Port Vale v Sutton United
Bradford City v Middlesbrough
Bournemouth v Stoke City
Lincoln City v West Ham
Brentford v Arsenal
Chelsea v Brighton
Salford City v Burnley
Fulham v Norwich City
Blackburn Rovers v Cardiff City
Liverpool v Leicester City
Newcastle United v Manchester City
Mansfield Town v Peterborough United
-- Courtesy of BBC Sport