The issue centres on arrangements made for players who have been loaned to Tynecastle from FBK Kaunas, a Lithuanian team also backed by Hearts owner Vladimir Romanov.
Hearts revealed the impending case in a brochure handed out to supporters about their bid to raise £1.79m through a share issue.
Since Romanov brought the club in 2005, an estimated 19 players have featured for Hearts as part of a loan agreement with Kanuas.
Captain Marius Zaliukas was initially on a temporary deal before making his stay permanent, while former players such as Bruno Aguiar and Marian Kello also moved to Edinburgh as part of loan agreements.
Privately, Hearts are keen to play down any comparison with the benefit trust scheme at Rangers, which is still being probed by the SPL.
Under the sub- heading "Risk Factors" in the brochure, Hearts state: "Heart of Midlothian plc are subject to a significant ongoing dispute with HM Revenue & Customs which, if it ultimately goes against the company, could have a dramatically negative effect on the company.
"Specifically, HMRC have claimed unpaid tax liabilities of circa £1.75m (excluding interest and penalties) 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 are successful in challenging the claims. The claims will be heard by the relevant tax tribunal in November 2012."