Butcher's men currently sit second in the Clydesdale Bank Premier League standings - behind champions Celtic - thanks to an impressive run of results.
The Highlanders will be hoping for further success by booking their place in the Scottish Communities League Cup final but must overcome a Hearts side desperate to add to the William Hill Scottish Cup they won last term.
McGlynn was not expecting the rise of Inverness this season but admits Saturday's opponents deserve a great deal of credit.
The Jambos boss said: "I would imagine the fact they're sitting second top of the table would be quite a surprise to most people.
"In recent years, they have been up and down to a certain extent.
"You would probably half expect them to float around in the bottom six and maybe be fighting relegation every other year, which has been the case.
"So, for them to be doing so well, is great credit to them and you've got to give massive credit to Terry Butcher and Maurice Malpas and all the people up at Inverness.
"Terry Butcher must be in line for the manager of the year. Neil Lennon will be fighting him with the European thing that Celtic are doing.
"But their achievement up until now has been fantastic. Yes, I'm surprised where they're sitting right now but they're there on merit and they deserve it."
Asked if Inverness are favourites heading into the semi-final, McGlynn said: "I'm not sure. It's an awkward one because Hearts are the bigger football club but, at the moment, Inverness are the ones who are doing particularly well."
Hearts' financial problems have been well-documented and McGlynn would love nothing more than to reach a Hampden final in what has been a turbulent campaign.
He said: "It would be a massive boost in a transitional period.
"There is so much going on off the park, a lot of negativity, and it would be great to get to another cup final.
"It would lift morale and the financial boost the club would get as well would be a massive bonus. We've got loads to gain from getting to the final."
McGlynn quit Raith Rovers to take over the Tynecastle hotseat in the summer, weeks after Hearts triumphed over Edinburgh rivals Hibernian to win the Scottish Cup.
He added: "From a purely personal point of view, it would be great to take Hearts to a cup final and go to Hampden.
"A few of them played in the Scottish Cup final and they must have enjoyed it so there is a motivation for others to try to get to that same stage and try to win a cup as well.
"There is motivation for individuals as well."
Meanwhile, McGlynn has confirmed Liverpool striker Michael Ngoo is one of a number of players on his radar.
He has already recruited Reds defender Danny Wilson on loan and could be set to make another Anfield swoop for a loan move for 20-year-old Ngoo.
McGlynn said: "He is one of a number that we have been looking at.
"We have been looking at strikers.
"It has been our Achilles heel this season, getting the ball in the back of the net.
"So it would be nice if we could freshen things up."
Asked if he could have a new recruit in place in time for Saturday's clash with Inverness, he said: "You never know."