Celtic will have to overcome Morton if they are to keep their hopes of a domestic double alive, after being drawn against the Greenock side in the last eight of the Scottish Cup.
Mark Warburton's Rangers will face either Dundee or Dumbarton at Ibrox if they can win their replay against Kilmarnock next week.
Meanwhile, Edinburgh rivals Hearts and Hibernian will fight it out in their replay at Easter Road for the chance of a home tie against Cup holders Inverness.
Ronny Deila's side reached the quarter-final stage after overcoming non-league minnows East Kilbride 2-0 on Sunday.
The quarter-final line-up is completed by Premiership outfit Ross County entertaining Dundee United.
All ties will be played on the weekend of 5th and 6th March.
Scottish Cup Quarter-Final draw in full:
Celtic v Greenock Morton
Hibernian/Hearts v Inverness
Kilmarnock/Rangers v Dundee/Dumbarton
Ross County v Dundee United
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