Next Saturday's game might be the 138-year-old club's last after owner Vladimir Romanov admitted the Tynecastle club faces a winding-up order about £450,000 due to Her Majesty's Revenue and Customs (HMRC).
The latest crisis to engulf Scottish football came nine months after the Edinburgh team's former Scottish Premier League (SPL) rivals Rangers went into administration over an unpaid tax and PAYE bill.
First Division Dunfermline recently denied rumours about its financial stability after some of the club's staff were not paid their wages, and Falkirk reportedly needed a cash injection to complete last season.
A Government spokesman said: "The Scottish Government stands ready to assist in any way it can, including making contact with HMRC if necessary.
"It is in everyone's interests to find a solution which ensures Hearts can continue in business while also meeting their obligations to the tax authorities."
The Edinburgh club's controversial Lithuanian owner, Mr Romanov, appealed to fans to provide the club with emergency backing to avoid the prospect of administration. He said he was not employing scaremongering tactics and they were genuinely attempting to avoid the fate of Rangers, which went into administration in February.
The club said: "This is not so much a request as a necessity. Without the support of fans there is, as we issue this note, a real risk Heart of Midlothian Football Club could possibly play its last game next Saturday, November 17, against St Mirren."
Tom Harris, secretary of the Bonnyrigg Hearts Supporters' Club said the club had been run disgracefully. He said: "I fear the worst now and I am completely gutted. It might not be the worst thing to go back to the start, with no debt and no foreign owner," he said.
"I have supported the club all my life and all you ever hear about them in the media, apart from the Scottish Cup victory, is about mismanagement, managers being sacked, contract issues and HMRC. The way the club has been run in the last five or 10 years is nothing short of disgraceful."
Mr Harris, 51, added: "They have had such great times over the years, but I have recently had the heart kicked out of me following them.
"I can't believe they are coming to the fans asking them to bail them out when it is mismanagement that has got us there in the first place."
The taxman lodged a petition to take Rangers into administration over the non-payment of £9 million PAYE and VAT which sparked financial meltdown at the Ibrox club.
Hearts had originally said they were attempting to negotiate a payment plan with the taxman, but then made a desperate appeal to fans to invest and save the club. The club urged fans to buy tickets for themselves and a friend for future home games against St Mirren, Celtic on November 28 and Aberdeen on
December 8, and to invest in a recently launched share issue, and buy a minimum of £110 of shares in the club.
Earlier, former Hearts legend John Robertson warned his former team could go bust if fans do not support the share issue, which aims to raise £1.79m.
The club said: "Discussions on whose name is above the door, talk about how the money has been spent and debate on whether the investment in silverware has been appropriate is all natural but quite simply worthless at this moment in time.
"The only valid debate now is how can you help the club. Is the club worth less than £110?"
HMRC has claimed unpaid tax liabilities in the region of £1.75m relating to loan agreements for a batch of players who joined Hearts from Lithuanian club Kaunas, who were then run by Mr Romanov.
Earlier this week, Dunfermline chairman John Yorkston said his club had resolved budgetary issues following problems paying staff wages.