Alloa Athletic await the winners of East Fife v Rangers and Livingston take on Stranraer in the semi-finals of the Petrofac Training Cup.
Livi's home tie with Stranraer is on Sunday 12 October and will be shown live on BBC ALBA.
East Fife's rearranged quarter-final with Rangers is scheduled for 21 October.
The Scottish Professional Football League will confirm dates and times for the second semi-final "in due course".
All three of Saturday's quarter-finals ended in 1-0 scorelines with Livi overcoming Peterhead after extra-time, League One Stranraer beating Championship side Falkirk and Alloa winning at Greenock Morton.
Livingston assistant manager Mark Burchill said: "We've been away a couple of times so far this season so a home tie is what we were looking for.
"For me it is a priority at the moment. We have to be realistic that with our budget we won't be competing to win the Championship, although we want to be near the play-offs. As a player or manager you want to try and win trophies so this is top of the agenda at the minute.
"I've watched Stranraer a couple of times in the last 18 months and I think Stevie Aitken is a top manager. He's done a lot with Stranraer during the time he's been in charge."
Stranraer captain Frank McKeown explained getting the semi-finals was "massive for the club".
"Last year we proved we can be underdogs against the bigger teams," he said. "We drew at Ibrox, scored three at Hibs, took Inverness to a replay and beat Ross County. This year we beat Falkirk and ran Ross County close [in the League Cup]."
Alloa manager Barry Smith believes being in the semi-final gives the Wasps "good exposure"
"At this stage of the competition it will be a difficult game no matter what," he said. "It would be disrespectful to East Fife to rule them out.
"We have to turn up on the day and make sure we get to the final.
And Rangers goalkeeper Steve Simonsen added: "It is a weird one in that we are playing catch up but having witnessed the draw we will hopefully know a bit about Alloa as the league tie will have taken place.
"The game will be difficult on their ground and their [artificial] surface. We've played on a few different surfaces such as grass and 3G so we will be already for it if it comes.
"We had a major disappointment last season [losing the final to Raith Rovers] so we hope to go one better than that."
Livingston v Stranraer (Live on BBC ALBA, kick-off 16:05 BST)
Alloa Athletic v East Fife or Rangers