The Tynecastle club need creditors to agree to release the 50% share-holding that is held by the collapsed Lithuanian investment company for a fee of around £50,000.
The transfer of the stake to Ann Budge's holding company (BIDCO) is regarded as one of the last significant hurdles still to be overcome in what has been a complex and protracted administration process for Hearts. UBIG agreed to hand over the share-holding following discussions at the beginning of February but that decision must also be ratified by their creditors.
Budge - a millionaire businesswoman and Hearts season-ticket holder - is funding the £2.5m for Ukio Bankas' 29.9% stake personally.
Former Hearts owner Vladimir Romanov's fallen bank was due £15.5m of the club's total £28.5m arrears, while he also held the club's Tynecastle home as a security against its debt. UBIG, another of Romanov's former companies, were owed £8.2m.
However, even if Hearts' administrators, BDO, are given the result they are looking for following the creditors meeting next week, it could still be a matter of weeks before Budge assumes control at Tynecastle.
It is understood that April is the earliest time that the new owner could take charge at the Edinburgh club.
Budge will manage Hearts for a minimum of five years before she hands over the majority shareholding to the Foundation of Hearts, the group financed by more than 8000 fans making monthly direct debit contributions.
Hearts were placed in administration on June 19 last year and made four players and 13 non-playing staff redundant immediately as a consequence.