For sale with debts totalling £1.5m, the club have been in court three times over unpaid council bills and faced two winding-up orders over unpaid tax.
Stirling Meerkats is one possible new name for the club.
That idea came about after the fans group, which has been endorsed by tennis star Andy Murray and Real Madrid's Cristiano Ronaldo, discussed selling the naming rights for the club.
Stirling Albion Supporters Trust lodged its fresh bid to buy the newly-promoted club last month.
BBC Scotland learned that it made an offer of around £300,000.
A similar bid had been rejected by chairman Peter McKenzie, who has long been subsidising the club, last summer.
Last year, the local council took action to recover £67,000 in unpaid rent and rates for use of Forthbank Stadium.
That figure has risen to £100,000 and legal proceedings were opened last month at Stirling Sheriff Court.
In May, the 84-year-old McKenzie made a £41,000 payment to save the club from liquidation and HM Revenue and Customs received a further £48,000 in November.
McKenzie announced in June 2008 that he wanted to step down as chairman and guarantor and make his majority shareholding in the club available for sale to any interested parties.
Source: BBC Sport
Source: BBC Sport