Hearts director Sergejus Fedotovas has claimed the club were on the road to fending off the immediate threat of closure and revealed talks were ongoing over a 'short-term fix' from Vladimir Romanov.
But Fedotovas warned much more money was still needed to meet a £450,000 tax bill. Hearts were presented with a winding-up order on Tuesday by Her Majesty's Revenue and Customs, the latest in a long line of such petitions.
The William Hill Scottish Cup holders paid off the most recent one in February but majority shareholder Romanov's UBIG investment vehicle is believed to have stopped funding the club since then. And Fedotovas, the closest figure to Romanov on the Hearts board, continued to urge fans to take control of the situation.
Fans were urged to buy tickets for three forthcoming home matches and subscribe to a share issue after the board warned on Wednesday that the visit of St Mirren a week from Saturday could be the club's last match.
"We are having a good response from the fans, from the people who really care about this club," Fedotovas said at Tynecastle on Friday. "I need to say thank you to everyone who has come to help us out. I'm hoping more people will continue to come and with their help we will be able to put this club in a safe zone.
"It's far from enough at the moment but the progress is good and if we continue like this we'll be fine."
The Lithuanian added: "We have been speaking to the companies of Mr Romanov and we have had some promising response. They say they will look at ways to help us out. Obviously not immediately, they require a certain time.
"I would not take that for granted but at least they are looking at ways to help us. At the end of the day any funding will have to be paid back - if we are able to get a fix it will be a short-term fix. So I think the best solution is for supporters to take this club into their own hands and ensure it will be here for many, many years."
Hearts have less than seven days to pay HMRC or face liquidation, although they could stave off that danger by voluntarily going into administration before then if they cannot pay.
When asked if administration was inevitable, Fedotovas said: "I have never thought about this and my priority is finding a solution, and I strongly believe a solution will be there."