Swansea are the last under-21 side left in the Trophy after four academy teams were knocked out on Tuesday.
Oxford United will play the winner of the final third-round game between Bradford and Cheltenham, which takes place on 17 January.
Meanwhile, Mansfield host League Two rivals Wycombe and Luton have been drawn at home against Yeovil.
The quarter-finals take place in the week beginning 23 January.
Mansfield v Wycombe
Swansea City U21s v Coventry
Oxford v Cheltenham or Bradford
Luton v Yeovil
Swansea City Under-21s will play League One Coventry City at home in the quarter-finals of the EFL Trophy.