Bankers believe that if Romanov's Ukio Bankas goes under, sister company Ukio Banko Investicine Grupe (UBIG) – which owns the Tynecastle club – would be affected.
Hearts said the Ukio Bankas collapse would have little effect on the day to day running of the Edinburgh club.
But a Lithuanian banking source said Ukio's plight could have a "direct impact" on UBIG, of which Romanov is chairman and said to be part owner.
Supporters are expected to have a clearer picture within days of the fate of Ukio, currently in temporary administration.
It is hoped the temporary administrator's report will be completed by Friday and officials are set to work through the weekend to take a decision.
Supporters' groups are said to be working behind the scenes to help "secure the future of the club" .
It was reported that UBIG recently used a new Lithuanian law allowing the company to pledge all of its assets as collateral.
A Hearts source said it was unclear what the long-term effect would be on Romanov's personal wealth, described as "weakened".
Labour peer and Hearts fan Lord Foulkes said: "Hearts are now moving into profitability and represent an asset rather than a liability. It is important that the administrator's action recognises this and protects the club."