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.
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Full Checkatrade Trophy Round Three draw:
Northern section
Rochdale v Manchester City U21s
Sunderland v Newcastle U21s
Accrington v Bury
Port Vale v Shrewsbury
Southern section:
Southend v Portsmouth
Chelsea U21s v Peterborough
Cheltenham v Oxford or Tottenham U21s
Northampton v Bristol Rovers