Holders Celtic could face rivals Rangers in the semi-final of the William Hill Scottish Cup.
Rangers and Aberdeen will play their quarter-final replay on Tuesday, March 12 at Ibrox after a 1-1 draw at Pittodrie on Sunday - and the winner will face Celtic at Hampden.
The other Scottish Cup semi-final clash sees Inverness Caledonian Thistle play either Hearts or Partick Thistle.
Hearts and Thistle will replay their quarter-final tie on Tuesday, March 12 at Tynecastle after a 1-1 draw at Firhill on Monday night.
The Scottish Cup semi-final ties are scheduled for the weekend of Saturday, April 13.
Scotland national team coach James McFadden, who helped make the draw alongside Twin Atlantic's frontman Sam McTrusty, said: “We could potentially see the two Glasgow sides go up against each other, although Aberdeen will have something to say about that, so it’s interesting.
"And Inverness will be hoping Partick Thistle can cause an upset against Hearts in the replay. John Robertson said before the game that he didn’t want Hearts because they dealt Inverness a heavy blow at the start of the season. Whoever is in that fixture could have a great chance of getting to the final.”
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