The Edinburgh club have vowed to 'robustly defend' their stance against Her Majesty's Revenue and Customs next month when a tax tribunal reviews the case which was revealed in their share issue brochure.
The dispute relates to a loan agreement for a number of players between Hearts and Lithuanian club Kaunas, who were then run by Vladimir Romanov, the Hearts majority shareholder since 2005.
But Hearts insist the situation was no different to any other loan, where parent clubs often meet wage demands.
The Hearts share issue brochure states: "Heart of Midlothian plc are subject to a significant ongoing dispute with HM Revenue and Customs which, if it ultimately goes against the company, could have a dramatically negative effect on the company.
"Specifically, HMRC has claimed unpaid tax liabilities of circa £1.75 million in relation to the arrangements between the company and Kaunas FC in relation to certain players who were loaned to the company by Kaunas FC.
"The directors are attempting to robustly defend those claims but the burden of proof is on the company and the tax will be payable unless the company is successful in challenging the claims."
This is the latest financial issue for the club to contend with as the SPL placed Hearts under a fresh transfer embargo last week after players and staff were not paid on time for a second successive month.