Holders Celtic will visit Partick Thistle in the Premier Sports Cup quarter-finals, while Rangers host either Hibernian or Livingston.
Aberdeen take on Motherwell at Pittodrie and St Mirren head to either Kilmarnock or Dundee United.
The ties will take place on the weekend of 20-21 September.
Thistle, managed by former Celtic defender Mark Wilson, are the sole non-Premiership club left in the competition and advanced with a 2-0 win over Ayr United.
Celtic began their trophy defence with a 4-1 win over Falkirk on Friday night, while on Saturday Rangers saw off third-tier Alloa Athletic 4-2.
St Mirren edged past Hearts on penalties and Aberdeen eased to a 3-0 victory at Championship side Greenock Morton.
In the remaining last-16 matches, Kilmarnock host Dundee United on Sunday and Hibernian visit Livingston.
