Hearts joint-administrator Bryan Jackson expressed concern at the weekend after a bid was made to UBIG for its 50 per cent stake in the club.
UBIG abstained from the vote on the Foundation's successful Company Voluntary Arrangement offer on Friday but the proposal is dependent on the fans' group acquiring the bankrupt Lithuanian firm's shares.
The firm would receive no money from the Foundation of Hearts but Borders-based businessman Bob Jamieson claims he has offered cash for its shareholding.
A Foundation of Hearts statement read: "We note the comments from BDO's Bryan Jackson in Sunday's newspapers and share his concern.
"This is a very complicated and delicate situation and we would urge any third party who is attempting to place an unfunded and fanciful rival bid to reflect on the potential damage this could do to the CVA process.
"This is too important to the future of HMFC to have a Walter Mitty character destabilise the progress of getting the club out of administration because of a desire for publicity or attention."
The £2.5million put up for the CVA would go to Ukio Bankas, which holds a security over Tynecastle and a 29 per cent stake in Hearts. The firm is also in administration.
Striking a deal with UBIG could leave Jamieson with a 50 per cent stake in a liquidated club as the Foundation's CVA deal is dependent on UBIG handing over its shares.
Jamieson described the Foundation's claims as "nonsense" and told the Herald: "It's not fanciful, I can assure you."
- Bob Jamieson
- Company Voluntary Arrangement
- Bryan Jackson