The stricken Tynecastle club have been unable to progress their battle to escape administration while there was uncertainty over the future of 50-per-cent stakeholder UBIG, itself declared bankrupt.
The Kaunas-based investment firm - once controlled by former Jambos owner Vladimir Romanov - is still waiting for a bankruptcy administrator to be appointed, with a court hearing set for Thursday.
But now the man running Ukio Bankas - another one-time Romanov venture, also now insolvent - has told Hearts administrator Bryan Jackson of BDO he can go ahead and start the process of negotiating a pence-in-the-pound Company Voluntary Arrangement with the club's creditors.
Ukio Bankas, which owns 29.9 per cent of the club and holds a floating charge on the stadium, and UBIG are owed around £24million, with around £4.4m owed to other companies.
BDO has already appointed fans' group the Foundation of Hearts as preferred bidders but trouble-shooter Jackson said the club are not out of the woods yet.
He said: "This is positive news as it means that we can progress the CVA process immediately by initiating meetings of the creditors and shareholders. We will also be able to begin the formal acceptance of the Foundation of Hearts bid and legally agree terms.
"I would urge caution however that, although this is a further step in the right direction, there is still some way to go. There are a number of issues to be clarified and concerns addressed but we are at least progressing once more."
Gintaras Adomonis, the administrator now running Ukio Bankas' operations, added: "The zeal and tenacity of the fans have persuaded us that the process of CVA should be launched as soon as possible by the administrators of Heart of Midlothian FC.
"We are still far away from the end of the legal process which we all shall endure, but this is a step forward nevertheless."
The Hearts support bought over 10,000 season tickets to help the club survive the summer but Jackson has now appealed to them to continue their backing.
"Although I am sure the fans are sick of hearing this, I cannot stress enough how important it is that they continue their extraordinary support for their club," he said.
"The fans, the staff, the players, the management and the FoH have all been outstanding over the last few months in keeping the club going but it needs to carry on. We still need to keep fans coming to matches and money flowing through the club to ensure that we have sufficient funds to push the CVA process forward."