The Reds’ reward for beating MK Dons 3-1 on Saturday is a trip to the Etihad to face the 2011 FA Cup winners.
It might be unthinkable that David Flitcroft’s side should beat City - who on Sunday thrashed Leeds United 4-0 in the fifth round - but in reaching a Wembley semi-final in 2008, the Reds defeated Liverpool and Chelsea.
FA Cup quarter-final draw:
Oldham/Everton v Wigan
Manchester City v Barnsley
Manchester United/Reading v Middlesbrough/Chelsea
Millwall v Blackburn
Ties to be played on the weekend of March 9 and 10.