Hearts expect to stave off the threat of administration by making a tax payment in the "very near future".
Newspaper reports on Tuesday claimed Hearts have seven days to settle a £100,000 debt to Her Majesty's Revenue and Customs or face a winding-up order.
But a spokesman for the SPL club played down those suggestions, saying: "We are in dialogue with HMRC and expect to make payment in the very near future."
Hearts were forced to seek the help of supporters as recently as December to pay a previous tax bill, while a repayment plan was agreed for a third tax debt.
Overall debt is estimated at £25m - although one of the club's two main creditors is now bankrupt and the other has claimed insolvency.
Tynecastle director Sergejus Fedotovas this month sent out a letter urging fans to renew season tickets despite the club's financial problems.
It read: "Looking forward, we are aiming to resolve all the financial issues before the campaign kicks off in August and will dedicate special attention to the football planning with a view to improving results for next season.
"The board aims to resolve the ownership and debt situation before the new season starts and we're also aiming to reshape the team to improve the areas we feel have been lacking.
"We'd like to ask for your continued support in helping us to attract the best players to the club in order to regain our position as domestic trophy winners and qualifiers for European competitions.
"The best way you can do this is by purchasing a season ticket. This is the one single most important action that you as a supporter of the club can take."