Hearts "will be taking further advice" should they be "expelled" from the Scottish Premiership, says Ann Budge.
A lack of top-flight support means reconstruction and a larger top league will not be put in place this summer.
And Hearts, four points adrift at the bottom, face relegation if the 2019-20 Premiership cannot be completed.
Chair Budge insists she will look at "what options are open to us and to other clubs in the same position, to formally challenge this outcome".
"I am bitterly disappointed, although sadly not surprised, that there is insufficient support from Premiership clubs to expand the top league," Budge told the Hearts website.
"It is fundamentally wrong that any club should be unfairly penalised by exceptional decisions that have had to be taken to deal with the current crisis. I would stand by that view, regardless of Hearts' own position.
"To pour more financial hardship on specific clubs, given what we are all going through both now and for the foreseeable future, is both outrageous and shameful."
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All Scottish football was suspended in mid-March because of coronavirus and SPFL clubs passed a resolution in April to end the Championship and Leagues One and Two early. As a result, Partick Thistle and Stranraer finished bottom of the second and third tiers and face demotion.
The resolution also gave the the SPFL board the power to declare the top flight over if the outstanding 49 fixtures cannot be completed.
A league reconstruction panel, co-chaired by Budge, discussed changing the current 12-10-10-10 model to three leagues of 14 or a 14-14-16 set-up, with the latter option including the Highland and Lowland League champions. Both would have given Thistle, Stranraer and potentially Hearts a reprieve from relegation.
Any plan would need a majority of Premiership clubs to back it for it to stand any chance of being passed by all SPFL clubs. However, at Friday's meeting of the current 12 top-flight sides and Championship winners Dundee United, it emerged most were against change.
Budge dismissed talk of reconstruction being a "distraction" as "incredibly sanctimonious" and believes clubs are against change because of the implications it may have for next season's live broadcast contract.
"Clubs are worried," said Budge. "They do not want to do anything that might in any way impact a major income stream.
"The value of the Sky contract is being held out as being under major threat if any changes to the league are made. Personally, I do not accept that this is the huge problem it is being assumed to be."
Budge also cited a "missed opportunity" to end the advent of teams playing each other four times a season "that drives so many supporters away from attending games" and revealed that the reconstruction task force had hoped to implement players' input.
"There was a genuine optimism that agreement could be reached," she added.
"Our objective should have been to stand together to protect each other. This would have demonstrated genuine leadership for the first time in many weeks."