Championship outfit Preston will be the first team to attempt to end City's bid for a second straight domestic treble when they welcome the Premier League champions to Deepdale.
Alex Neil's men thrashed 2013 runners-up Bradford 4-0 in the second round on Tuesday to progress, but will next face a City team who scored 27 goals in six games against lower-league opposition last season.
European champions Liverpool were beaten by Chelsea in the third round last term, but will be expected to find life easier at League One outfit MK Dons.
Jurgen Klopp's side are the record eight-time winners of the competition.
Elsewhere, the draw threw up the first south-coast derby since April 2012 between bitter rivals Portsmouth and Southampton.
Third-division Portsmouth will host Ralph Hasenhuttl's Saints at Fratton Park following Wednesday's 2-0 win at Championship club QPR.
Last season's runners-up Chelsea host either Grimsby or Macclesfield, whose game was abandoned on Tuesday due to heavy rain, while Arsenal welcome Nottingham Forest to the Emirates Stadium and Tottenham visit Colchester.
Manchester United will take on near neighbours Rochdale at Old Trafford.
The games will be played during the week beginning on September 23.
Wolves v Reading
Oxford United v West Ham
Watford v Swansea City
Brighton v Aston Villa
Sheffield United v Sunderland
Colchester United v Tottenham
Portsmouth v Southampton
Burton v Bournemouth
Preston v Manchester City
MK Dons v Liverpool
Manchester United v Rochdale
Luton v Leicester
Chelsea v Grimsby/Macclesfield
Sheffield Wednesday v Everton
Arsenal v Nottingham Forest
Crawley Town v Stoke City