Former Kilmarnock chairman Jamie Moffat has offered to write off a loan of almost £2m made to the club, thus reducing their debt to £9m.
But the club must first find someone to guarantee the £200,000 presently underwritten by him to their bank.
Kilmarnock chairman Michael Johnston believes that the move could remove a barrier to new investment in the club.
"I hope to find a willing guarantor to replace Jamie in the weeks ahead," he said in a club statement.
"Jamie's proposal could facilitate a radical improvement in the club's finances, a gesture in keeping with his family's legacy as the greatest supporters of Kilmarnock Football Club in its 140-year history."
Johnston, who revealed the offer following the Scottish Premier League club's annual meeting, paid tribute to the Moffat family.
"Over the last fifteen years or so, the Moffat Family have made a number of remarkable contributions, financial and otherwise, in order to maintain Kilmarnock's position in the top flight of Scottish professional football.
"The Moffat Stand, largely funded by the family, stands as a lasting tribute to their generosity."
Jim Moffat led the club to Scottish Cup success in 1997 but died the following year, after which his son became a director then chairman.
"The Moffat family's generosity continued with further significant investment in shares and loans at critical moments in order to secure the club's financial wellbeing," said Johnston.
"Part of this support is recognised in the club's balance sheet in terms of the director's loan account, amounting to almost £1.8m.
"This 'soft loan' has remained in place for several years now with no capital reduction or loan interest being sought."
Johnston said that Moffat's latest offer would help the club once more.
"The existence of the director's loan account is, perhaps, an obstacle to new investment in the club by interested parties," said the present chairman..
"With this in mind, Jamie has proposed that the loan be written off on the proviso that he is relieved of his guarantee to the Bank of Scotland in the sum of £200,000.
"Clearly, the club's balance sheet would be greatly improved by the removal of the director's loan account.
"That may, in turn, lead to new investment in the club of a substantial nature which would replicate the step change enjoyed under the late Jim Moffat."
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