Hearts director Sergejus Fedotovas has warned fans the club could face another do-or-die situation if more do not buy shares.
The club have now raised more than £800,000 in a share issue scheme that was launched last month and closes on December 19.
Hearts recently averted a winding-up order after paying Her Majesty's Revenue and Customs a £450,000 bill, and they have settled another issue with the tax authority by agreeing to pay £1.5million over three years.
Players voluntarily deferred their wages last month but these are now up to date and Fedotovas confirmed today that they would be able to pay this month's wages by the December 16 deadline.
But Fedotovas continued to warn fans of the dangers ahead by stating they were facing a £1million deficit.
He added: "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."
The warning comes in the week that Lithuanian striker Arturas Rimkevicius, who scored 35 league goals for FK Siauliai last season, arrived at Tynecastle on trial.
Hearts are under a Scottish Premier League transfer embargo until December 23 over delayed wage payments, and will expect that to be lifted after this month's salaries are paid in full.
However, it is understood that some players are still awaiting bonus money due from their William Hill Scottish Cup triumph in May.
Fedotovas said in a lengthy statement on the club website: "It is premature to speak about any transfer business as it is never known in advance if deals will happen, particularly with staff salaries and monies due to the tax man in January.
"It goes without saying that if we sell players without suitable replacements being available, our league position could suffer."
Fedotovas revealed 3,200 fans had contributed to the share scheme, which aims to raise £1.79million.
"But we had 100,000 supporters celebrating in the streets of our capital city after our Scottish Cup victory in May, and have 8,500 season ticket holders," he added.
"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.
"We may disagree about the future with all those criticising the club now but we must preserve what we have today in order to have a future."
Talks continued between Hearts and Supporters Direct Scotland today, at the request of Hearts.
Head of Supporters Direct Scotland Paul Goodwin said: "I was greatly encouraged at the amount of progress made today and with the club's willingness to continue to explore the options available.
"Supporters Direct Scotland believes that as we continue to get a better understanding of the options available to the club, there is a fantastic opportunity that a solution can be found that will be acceptable to the whole Hearts community as well as the current owner.
"Today was about looking in detail at some of the concepts that Supporters Direct Scotland had previously presented, and for the club to get to a position where there is a framework for future meetings that will undoubtedly follow in the coming weeks."
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