But Cricket New South Wales Chief Executive Lee Germon said the state governing body had sent a counter-proposal to CA and other member states which involved self-funding mechanisms.
"Our position is unchanged from ... a few weeks ago," the former New Zealand test captain told reporters in Sydney on Wednesday.
"We still do not believe that the sale of the BBL clubs is the right approach here.
"We are in fierce agreement with Cricket Australia that we need to invest in the BBL, we need to grow the BBL, we need our best players playing in the BBL and in a window that allows that."
New South Wales hosts two BBL teams, Sydney Sixers and Sydney Thunder.
Queensland Cricket, which hosts Brisbane Heat, said on Wednesday it had made no final decision following a board meeting and would seek further information from CA.
The other four member states - Victoria, South Australia, Tasmania and Western Australia - are seen as broadly supportive of private investment but the lack of consensus is a major blow for CA.
"We ... remain open to discussing any questions or concerns about this model," CA boss Todd Greenberg said in a statement.
"This process remains respectful and collaborative and with the best interests of Australian cricket the key consideration of all involved."
The privatisation push has been driven by CA Chairman Mike Baird and CEO Greenberg following a review by Boston Consulting Group last year.
CA hopes to raise up to AU$600 million (US$427 million) from the sale to future-proof the sport, boost its finances and improve Australia's competitiveness in T20 cricket.
CA reported a net deficit of AU$11.3 million for the 2024-25 financial year despite a jump in revenue from hosting the lucrative Border-Gavaskar series against powerhouse India.
Australia crashed out of the group stage at the recent T20 World Cup won by India, triggering acrimony on the home front.
Despite the potential for a major capital boost, influential cricket figures in Australia remain wary of private money.
Former test captain and talent development boss Greg Chappell said the BBL was a success and selling it off could mean a damaging loss of control for the game's local custodians.
"Australian cricket has long benefited from maintaining its autonomy," he wrote in a column published in the Sydney Morning Herald.
"Surrendering even part of that independence could have far-reaching consequences."
