The Edinburgh club have been issued with a winding-up order from Her Majesty's Revenue and Customs relating to a tax bill of £450,000 and are desperately trying to raise the money required to stay afloat.
With a number of clubs also thought to be in a fairly perilous financial position, McCoist is worried that others may go the way of Rangers who had to begin life again as a new company in the Irn-Bru Third Division after failing to meet their liabilities.
"It would be a disaster," said the Rangers manager when asked about the consequences of Hearts' demise, should it come to pass. "You hear so many rumours about other clubs that are running close to the wire. Looking at it and listening to other chairmen then unfortunately it might be a possibility [that clubs go to the wall] both from within and outside of the SPL.
"What happened to us, you would think, would be a warning to everybody. When some other clubs went into administration I would imagine the general consensus of opinion from a lot of people would have been 'well, that happens' and I include myself in that, but you don't think it's going to happen to a Rangers, Celtic, Manchester United or Liverpool; you just don't see that happening. So I think we are an absolute warning to everyone that it can happen no matter how big, small or successful you are."
McCoist, more than anyone, can empathise with John McGlynn, the embattled Hearts manager trying to keep his players focused on football while also serving as unofficial mouthpiece for the club, giving supporters assurance and guidance in equal measure.
The Rangers manager, whose side take on Peterhead at Ibrox this afternoon, described watching his club fall into administration and then liquidation as among the most traumatic periods of his career but hoped that McGlynn would not lose faith.
"You can never give up hope, that's the most important thing," he added. "I'm sure John's got good people around him which is vital and they will have to stick together. In many ways it does bring out the best in people a lot of the time. I think with a bit of guidance and luck they will come through it. I'm obviously very sympathetic towards their situation and will give John a phone just for a chat."