Speaking on the day fans group Save Our Hearts wrote an open letter to owner Vladimir Romanov asking the banker to make a "dignified exit" by handing over his majority shareholding to the consortium led by accountant Alex Mackie, McGlynn was reluctant to be drawn on the matter.
Romanov has already rejected a bid from the Foundation of Hearts, who want to bring the club under the control of the supporters.
"The manager and players can't get involved in that," said McGlynn. "We leave that to the people upstairs. The people in charge will do what they think is the right thing for the club. Whatever is best will come through. If you are a fan, you will want some say in it, no matter what club.
"Motherwell are doing something similar. It seems to be the way things are going but I'm not in a position to comment. I am an employee of HMFC and I will do the best I can on a day-to-day basis."
Save Our Hearts gave a ringing endorsement of the Foundation of Hearts' objectives in an open letter that urged Romanov to stand aside. The supporters group was initially founded in 2004 with the aim of stopping then owner Chris Robinson's controversial plan to sell Tynecastle and use Murrayfield stadium as the club's home.
They have reformed in the wake of the club confessing that the recent winding-up order over a £450,000 tax bill pushed Hearts to the brink of extinction.
A section from the letter read: "Last Wednesday, the 'rollercoaster' that is Heart of Midlothian FC very nearly came off the rails. That is when the ride got a little bit too scary. I now think that both parties – the fans and you – want to get off.
"Vladimir, we know that you hold the traditions and history of this club in the highest regard. That is why we are now asking you to work together with the Foundation of Hearts so that 138 years of history can be preserved."
The Foundation of Hearts, meanwhile, have asked fans how much money – on a scale between £10 to £100 – they would be willing to contribute to a monthly membership, embracing a system similar to Barcelona's business model.