Currently the YJB holds the budget for custodial places in England and Wales.
Chair Frances Done spoke publicly for the first time on the issue at a conference in Nottingham last week, and called for the matter to be discussed with stakeholders including the Local Government Association.
Done said the "perverse incentives" created by the current system need to be addressed.
It is argued that making local authorities responsible for the cost of custody may incentivise them to make sure provision is available for those at risk of serious offending.
A YJB spokeswoman said the board is keen to get reactions from different stakeholders.
"We are not at a stage where this is a formal proposal but we are keen to get some views," she said.
The Youth Crime Action Plan, published in July 2008, has already proposed local authorities taking on the cost of putting children in court-ordered secure remand although this represents a fraction of the YJB's commissioning responsibility.
Done first outlined her thoughts on the issue during an interview with CYP Now earlier this year.
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