Neil Lennon's side, who lost last season's final, will be aiming to go one better this season.
The last four meeting will take place at Hampden Park.
Crisis-hit Hearts, who on Wednesday warned their game against St Mirren on November 17 could be their last after being presented with a winding-up order over a £450,000 tax debt, have been drawn to play Inverness with that match taking place at Easter Road.
The games are to be played on the weekend of January 26-27.







