Hearts were forced into administration earlier this month, with administrators BDO urging supporters to buy season tickets in a bid to aid the stricken Edinburgh outfit's cause. Fans raised more than £1million in a share issue last year to stave off a previous threat.
Pars supporters also rallied to keep their club alive after owner Gavin Masterton called in administrators in March with the club more than £8million in debt.
Paul Goodwin, head of Supporters Direct Scotland, said: "Hearts and Dunfermline fans have already made massive financial contributions to saving their clubs yet, at the moment, when it comes to any final deal to bring these clubs out of administration, they will be ignored.
"At Hearts, the fans contributed over £1million through a share issue in December and are now in the process of digging deep once again to bring in over £800,000 from season ticket sales.
"That is a staggering £1.8million spent to save the club in just over six months.
"At Dunfermline, it was touch and go whether liquidation could be avoided yet the fans rallied to raise hundreds of thousands of pounds to ensure the club continued trading, agreed to underwrite the administrators' fees and gave them £100,000 in terms of working cash to get through to the end of last season.
"Yet, as it stands, another bidder could come into either or both clubs without having contributed a penny to saving them and in turn have an immediate competitive advantage given the amount of money that both sets of fans have already spent.
"We believe it is essential that in any final deal for either of these clubs BDO, the administrator for both clubs, account for these vital financial and emotional contributions by both sets of fans when assessing prospective bids.
"It would be easy to see past the efforts of Pars United and the Foundation of Hearts and just accept the highest bid while ignoring the huge sums already put into the club to keep them alive. Fans bring with them more than just instant money, they bring credibility and proof that if you want a sustainable football club you need to have the fans with you."