Creditors can meet on November 22 to consider a B£2.5million offer from the Foundation of Hearts.
The deal would see the two major shareholders, Ukio Bankas and UBIG, hand over their combined 80 per cent shareholding.
Thae bank, which is also in administration, holds security over Tynecastle Stadium and the deal proposes this is also handed to the Foundation of Hearts' fan group. UBIG is also insolvent and a court hearing to appoint an administrator has been postponed several times.
The Foundation would take on the club's football debts of more than B£500,000 but none of the other minor creditors would receive a penny.
The Lithuanian institutions are owed about B£25million combined with the club's total debts closer to B£30million.
Foundation of Hearts chairman Ian Murray said: "We welcome the news that BDO is progressing the CVA for 22nd November and hope that there will be a positive outcome.
"There is much work to be done, and again I cannot stress enough the importance of supporters who have not yet signed up to FoH, and who are able to do so."