Barry Ferguson, the former Rangers captain, could take his Clyde team back to Ibrox in the Petrofac Training Cup.
The Broadwood club have been rewarded for their first-round win over Ayr United with a trip to face the winners of the August 5 tie between Rangers and Hibernian.
Hearts will travel to nearby Livingston, Stirling Albion face local rivals Alloa Athletic, while the Highland League champions Brora Rangers have received a home tie against East Fife following their impressive victory over Stenhousemuir.
Loading article content
Dunfermline or Raith v Falkirk
Brora Rangers v East Fife
Brechin City v Peterhead
Stirling Albion v Alloa Athletic
Livingston v Hearts
Rangers or Hibernian v Clyde
Morton v Berwick Rangers
Stranraer v Albion Rovers