Kilmarnock have a debt of more than £9million but chairman Michael Johnston is reported to have held negotiations with the club's bankers over a deal.
A group calling itself the Killie (Community) Working Party hopes to establish a Community Interest Company, in conjunction with Supporters Direct Scotland, to purchase the club.
A representative of the group, Gary Torbett, said: "We would like to acknowledge the work being undertaken by the chairman of Kilmarnock Football Club to make the club debt-free and would positively encourage him to make every effort to come to an agreement with the club bankers and other significant lenders to reduce the debt to zero.
"The Killie (Community) Working Party would like to make an offer to purchase the chairman's entire shareholding if this can be achieved."
Torbett added: "We see this move as a genuine step forward as we prepare to get our club back. Unfortunately there remains concern amongst supporters with the long-term position of the club and we firmly believe that fan and community ownership is where that lies rather than relying on a single majority shareholder who won't be around for ever."
The groups represented in the collective are the Killie Trust, the Kilmarnock FC Supporters Association, Minority shareholders in Kilmarnock FC, the Business Club and Young Kilmarnock.