Hearts are are at home to lower division opposition, either Westdyke or Dundee United.
If Hibs overcome St Johnstone in their postponed third-round tie, they will also host lower division opponents, Gartcairn.
Spartans have a tricker but winnable tie, with a trip to top-flight Aberdeen or Glasgow Women.
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Boroughmuir Thistle, fourth in SWPL2, might fancy their chances of an upset away to SWPL1 second-bottom side Partick Thistle.
Livingston also have a good draw. If they beat Montrose at home, they will take on Dryburgh Athletic or Kilmarnock at the Tony Macaroni Arena.
The games are scheduled for Sunday, February 13.
SWPL1 action resumes this weekend, with Hibs hosting Celtic, Hearts hosting Rangers and Spartans travelling to Aberdeen.