The match is scheduled to take place at Easter Road in the last weekend of January - with Celtic facing St Mirren at Hampden in the other fixture - but fans have been told they must purchase tickets for upcoming games and subscribe to a share issue so the club can see out the next week or so.
Hearts face continuing struggles if they do appease Her Majesty's Revenue and Customs, not least a separate tax bill of £1.75million that they are challenging at a tribunal, along with ongoing problems of meeting wage costs.
But McGlynn is optimistic Hearts will still be around to play the semi-final.
"We are here and we have done the draw for the semi-final," he said following the ceremony at Broughton High School in Edinburgh.
"Inverness at Easter Road is certainly one to look forward to. You have to be optimistic.
"It's a totally different situation from Rangers but Rangers are still here and they played in the quarter final and they've just won in the Scottish Cup.
"They are still here and I'm hoping Hearts are still going to be here when the semi-final comes around and we are playing Inverness at Easter Road in January."
Scottish Football League chief executive David Longmuir has witnessed similar problems among clubs in his domain and shared McGlynn's optimism.
Longmuir said: "It is very early days. The issue is for Hearts fans to rally round, and nurse the club through the next short period and I am sure the SPL will be doing their utmost to support their clubs.
"We have come through a difficult period in Scottish football but this is not new news in terms of clubs finding themselves in financial difficulties and I do feel that we have to make some fundamental strategic changes to the game, both structurally and financially to ensure that we never encounter these situations again.
"And having dealt with a few over the last five years we have a tried and tested process but at the moment it is too early to comment.
"Hearts have a future, they are a great club and I am sure the supporters will rally round.
"Today was about our League Cup draw, Hearts are in that draw and I fully expect them to perform well in the semi-final."
Inverness manager Terry Butcher was delighted to avoid Celtic but added: "I am concerned that one of the great sides of Scottish football is in trouble and hopefully they can resolve that. It is a sign of the times unfortunately.
"Hearts is a fantastic club. I have enjoyed playing against them many times as a player and as a manager so hopefully that will continue."
Meanwhile, St Mirren manager Danny Lennon is looking forward to testing his team against Celtic's Champions League heroes.
"At this stage it's all very, very good teams and Celtic are riding on a high from last night after beating Barcelona," Lennon said.
"We are just thankful the game is in two months' time and we can let them come down from that high.
"On a serious note, it's a wonderful occasion for us to look forward to.
"We are going to the national stadium and playing against the best in Scotland at this minute in time."
Celtic won 5-0 at St Mirren Park last month but Parkhead midfielder Joe Ledley will take nothing for granted in the semi-final.
"Every game is going to be very difficult," the Wales international said.
"We did well against them in the first game we played against them so hopefully we can continue that form and get a result."