Hearts have left the possibility of legal action open after the SPFL decision to halt the season resulted in the Edinburgh club being officially relegated from the Premiership.
Hearts, who have Northern Irish players Liam Boyce, Conor Washington, Michael Smith and Bobby Burns on their books, were bottom of the table when play stopped, four points adrift of Livingston with eight matches left to play.
Speaking shortly after the season was suspended back in March, owner Ann Budge said she would 'have to' take legal action if the club was demoted with no further games played.
Budge was given approval to work on a temporary reconstruction proposal that could see 14 teams in next season's top-flight, offering her side a reprieve from relegation.
Initial talks broke down although recent days have offered renewed hopes as the plan is back on the table following a meeting of Premiership clubs on Friday.
In a statement published shortly after Monday's decision was announced, Hearts underlined their hopes that a solution could be reached but did not rule out a legal challenge.
"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," the club said.
"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.
"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."