Talks between the club and The Pars Community (TPC) broke down in acrimonious fashion on Friday after the fans' group failed to secure acceptance of their offer to majority shareholder Gavin Masterton.
The club also received confirmation from Her Majesty's Revenue and Customs over a winding-up order, which gives them until March 26 to pay a £134,000 tax debt.
But chairman John Yorkston subsequently claimed he was confident they would meet the deadline and there was further optimism following a meeting on Saturday of the Dunfermline Athletic Steering Group, which was set up to allow director of football Jim Leishman and others to negotiate with supporters.
A statement on the club's official website read: "The Steering Group would like to confirm that a number of Dunfermline fans have expressed an interest in making substantial investments in the club.
"We can also confirm that the future ownership of the football club will be as per the proposal agreed with the club on Wednesday 13th March, which is a supporter led model and there will be no shares held by the Masterton family in the club.
"The current board are sufficiently comfortable with the proposals put forward by the Steering Group to allow due diligence to commence on Monday.
"Dependant on the outcome of this due diligence, the investment strategy will be concluded as quickly as possible.
"This could be the last realistic chance to save our club."