Hearts director Sergejus Fedotovas insists the club will suffer further financial problems unless more supporters are willing to buy shares.
The troubled Tynecastle club launched a share issue last month which has already raised £800,000 but that is due to close on 19 December.
Hearts recently averted a winding-up order after paying Her Majesty's Revenue and Customs a £450,000 bill, while they have also agreed to pay £1.5m over three years to the tax man over another outstanding bill.
Despite the efforts involved so far, Hearts are still facing a £1m deficit in their attempts to secure the club's long-term future.
Fedotovas said: "If we are not able to bridge the target for the share sales, the club will be in the same difficult position as we were in November but this time with no option for shares.
"I appreciate a lot of these people may still be reluctant to pledge their monetary support to help the club in our hour of need.
"If that is the case, I would urge every fan to ask themselves: 'Have I done all I can to help the club that means so much to me and people close to me?' If they are brave enough to answer 'no', then there is still time for them to act.
"But if they choose to wait, it may be a bad decision and there may be no return."
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