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Ms Budge's company Bidco (1874) Limited has now offered pound(s)2.5 million for
It said that would allow a company voluntary arrangement to be completed and to see the club's parent company exit administration.
Bidco said that while legal agreements are not yet in place, it believed the "rescue package" would see Hearts returned to "a position of financial stability".
As sole director, Ms Budge would take the chairman's seat at Hearts on a no-fee basis.
She would take over from controversial Lithuanian businessman and UBIG owner
A Barcelona-style membership scheme where many fans take a stake in the club is expected to remain central to the strategy. But Bidco said that, while there were plans for wider fan owner-ship, it would not be immediate.
There would be supporter representation on the new board.
The firm said it expected to hand over the majority ownership to the fans' group
It is intended that FoH will sign a legally binding agreement that it will transfer pound(s)1m to the club for working capital after the takeover is complete.
It would also provide further working capital support to the club for at least two years at a rate not less than pound(s)1.4m a year.
The fans group would also be expected to provide financial support to the club to enable the capital loan to be repaid in full.
The firm said it was "vital" that supporters understand that it is likely that pound(s)6m must be raised over five years to "achieve the objectives of saving the club over the long term and moving into supporter ownership".
Last week administrator BDO reached a draft deal with lawyers in
Hearts, at the foot of the Scottish Premiership, entered administration on
Multimillionaire IT guru and angel investor