Holders Celtic will face city rivals Rangers in the Scottish Cup last 16, should the latter beat Cove Rangers later on Sunday.
Steven Gerrard’s Scottish champions would welcome their Old Firm rivals – who have won the last four finals – on the weekend of 17/18 April.
Whoever prevails would play either St Johnstone or Clyde in the last eight.
Aberdeen will host Livingston in the only confirmed all-Premiership tie of the fourth round.
But each of the quarter-finals could be between top-flight teams, with Aberdeen v Dundee United another potential match-up should they win their respective ties.
All of the matches will be decided on the day, with extra time or penalties if needed.
Last 16 draw: Stranraer v Queen of the South or Hibernian; Motherwell v Greenock Morton; St Mirren v Inverness Caledonian Thistle; St Johnstone v Clyde; Rangers or Cove Rangers v Celtic; Aberdeen v Livingston; Forfar Athletic v Dundee United; Kilmarnock v Montrose.
Quarter-final draw: Rangers/Cove Rangers/Celtic v St Johnstone/Clyde; Kilmarnock/Montrose v St Mirren/Inverness Caledonian Thistle; Aberdeen/Livingston v Forfar Athletic/Dundee United; Stranraer/Queen of the South/Hibernian v Motherwell/Greenock Morton