After speculation that the separate gatherings of Ukio Bankas and UBIG would again be delayed, and subsequently lead to the Gorgie club being liquidated, BDO administrator Bryan Jackson and fans-backed group Foundation of Hearts are keeping their fingers crossed they will go ahead.
Jackson, who has said the club will run out of money at the end of this month, has flown out to be present but even if the meetings do take place it is understood that there continue to be mixed messages emanating from Lithuania about the likely outcomes.
Hearts need creditors of Ukio and UBIG to approve the transfer of their respective 29 and 50% shareholdings so the club can move closer to exiting administration.
Edinburgh IT businesswoman Ann Budge is personally funding the £2.5m company voluntary arrangement offer for Ukio's shareholding - which is secured against Tynecastle - for Foundation of Hearts.
But it is thought the Hearts season-ticket holder is growing increasingly frustrated by the protracted negotiations in Lithuania and there are suggestions she will reconsider her position should Hearts fail to secure the result they need in the Baltic state today.
The club's office staff were called to a meeting on Friday and were told that liquidation is inevitable should the creditors' meetings not go in their favour.
That would leave Hearts facing the prospect of starting life in League 2 as a 'newco'.
There was some positive news yesterday, however,
when it was reported that Siauliu Bankas - one of fallen investment company UBIG's main creditors - said they would approve the transfer
of the shares.
It was thought the bank had been unhappy at the prospect of UBIG, whose £8.2m debt was not secured, only receiving a sum in the region of £70,000 for their stake. However, Ilona Baranauskien, head of Siauliu's assets restructuring division, said: "Siauliu Bankas support the position of UBIG's administrator to transfer the shares to the new owner of Heart of Midlothian FC."