CA had set a mid-April deadline for the nation's six member states to indicate their support to sell 49% stakes in most BBL teams and 100% of one team each in Victoria and New South Wales.
New South Wales rejected CA's proposal while Queensland deferred its decision, saying it needed more information.
"Given CA does not currently have full alignment on the proposed next step with our members, some alternative options are being considered that require additional analysis and consideration with States, and that work is underway," CA said in a statement.
"Australian cricket remains united on the need to grow and continue investment in all aspects of the game and CA thanks the state associations and players for their engagement and collaboration in this project."
The lack of consensus is a major blow for CA Chairman Mike Baird and CEO Todd Greenberg, who spearheaded the privatisation push following a review by Boston Consulting Group last year.
CA had hoped to raise up to A$600 million to future-proof the sport, boost its finances and improve Australia's competitiveness in T20 cricket.
CA reported a net deficit of A$11.3 million for the 2024-25 financial year despite a hike in revenue from hosting the lucrative Border-Gavaskar series against powerhouse India.
Despite the potential for a major capital boost, influential cricket figures in Australia voiced opposition to opening the league to private money, saying it could mean a damaging loss of control for the game's local custodians.
