Ridsdale has been in talks with current owner Peter Doyle for several months and was in the directors' box for Saturday's 1-1 draw with Notts County.
The former Leeds chairman is backed by millionaire Tykes fan Patrick Cryne, the chief executive of the club's former sponsors iSoft.
It is believed that the pair will clear the Nationwide Division Two side's £5.2m debt to mortgage lenders Sterling and take the club out of administration.
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