Hearts are considering legal action following the "unjust" decision to relegate them from the Scottish Premiership.
The Edinburgh club will drop into the Championship after the SPFL opted to end to the 2019/20 Premiership season on Monday, with the campaign determined on a points per game average.
Hearts were four points adrift at the foot of the Premiership when the season was suspended on March 13, resulting in their second relegation in six years.
A statement from Hearts suggests they will challenge that decision, while they have also not given up on a restructuring of the league.
The statement read: "We have stated from the outset that we don't believe it is right that any club should be unfairly penalised because of the Covid-19 pandemic.
"It was previously indicated that league reconstruction would not generate enough support to pass a vote between member clubs. In recent days a number of positive talks have been held with both the SPFL and member clubs and this topic is currently being revisited.
"Hearts will shortly submit a member's resolution that we believe is a pragmatic solution to the issues the game currently faces and a way forward that the clubs can unite behind. It is our belief that this resolution, if supported, will provide an opportunity to avoid disproportionately disadvantaging - financially and otherwise - any club.
"This is possibly the final chance for our game to stand together, protect each other and not only survive but flourish in the aftermath of this terrible pandemic. Players from across all leagues have shown a desire for reconstruction and having already received support from some clubs we are hopeful that this resolution can positively progress Scottish football.
"As previously intimated the club has been taking legal advice throughout this process and are continuing to do so. We hope that the resolution being prepared will avoid the need to go down this route. Legal action would be both time consuming and expensive. However the cost to the club of relegation would outweigh these considerations.
"To our supporters, we thank you for showing patience and continuing to back the club. We will continue to fight against what we believe is an unjust outcome."
'Talks needed over Stendel future'
Hearts manager Daniel Stendel's agent, Timo Rodewald, has told Sky Sports News "plenty of discussions will need to take place" with the club following relegation from the Scottish Premiership.
Stendel's contract with Hearts contains a release clause on both sides which is triggered if Hearts suffer relegation.
Rodewald says he last spoke with Hearts owner Ann Budge at the end of last week about the manager's future, and is awaiting further correspondence from Budge before a decision can be made as to whether the German will continue at Tynecastle.
He confirmed Stendel "now technically has no contract" with Hearts, but that he is open to staying with the club "if certain things can be agreed and if the structure at the club can be improved.
Stendel joined Hearts in December 2019, replacing Craig Levein and opted to waive his wages entirely to help the club cope with the coronavirus pandemic.