Rangers will face a Scottish Cup fifth-round trip to Hibernian if they can defeat East Stirlingshire, while Celtic could be sent to Kilmarnock.Hibs' reward for crushing Inverness 3-0 in the fourth round on Saturday in new boss Mixu Paatelainen's first match is a probable home tie against the Gers.
Walter Smith's SPL leaders will make the trip to Easter Road next month if they overcome Third Division side East Stirling at Ibrox on Sunday.
Celtic, who beat Stirling Albion 3-0 at Parkhead, will travel to face the winners of the postponed clash between Airdrie and Killie.
All ties are due to be played on the weekend of February 2-3.
With weather taking a heavy toll on the fixture list, the fifth-round draw did not produce one confirmed fifth-round head-to-head.
St Mirren, who cruised to victory over Dumbarton at Love Street, will host Clyde or Dundee United.
Queen of the South, who snuffed out Linlithgow Rose's hopes, will travel to face either Morton or Gretna, who drew 2-2.
Hearts or Motherwell, who drew 2-2 at Tynecastle, were drawn at home against either Huntly or Dundee, whose match was postponed due to the big freeze which hit Scotland overnight.
Falkirk or Aberdeen, who also managed a 2-2 result, will have home advantage against Hamilton or Brechin, whose game ended in a 0-0 draw.
The remaining two ties feature clubs who were forced out of action by the weather.
Livingston or Cowdenbeath will meet Partick or last season's beaten finalists Dunfermline, while Cove Rangers or Ross County will tackle St Johnstone or Raith Rovers.
Scottish Cup fifth-round draw: Morton or Gretna v Queen of the South; Falkirk or Aberdeen v Hamilton or Brechin; Airdrie or Kilmarnock v Celtic; Hearts or Motherwell v Huntly or Dundee; Livingston or Cowdenbeath v Partick or Dunfermline; Hibernian v Rangers or East Stirlingshire; Cove Rangers or Ross County v St Johnstone or Raith Rovers; St Mirren v Clyde or Dundee United.
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