City booked a place in the knock-out phase after beating Barnsley on penalties in the previous round, while Rochdale progressed after a dramatic late win over Oldham.
The Blues started as one of 16 Under-21 teams competing in the 2018/19 instalment of the competition, with EDS boss Paul Harsley overseeing the squad.
The exact date and time of the game will be confirmed in the coming days.
Full Checkatrade Trophy Round Three draw:
Rochdale v Manchester City U21s
Sunderland v Newcastle U21s
Accrington v Bury
Port Vale v Shrewsbury
Southend v Portsmouth
Chelsea U21s v Peterborough
Cheltenham v Oxford or Tottenham U21s
Northampton v Bristol Rovers