Writing in Cafcass's annual report for 2015/16, Anthony Douglas, the organisation's chief executive, says increases in demand, in both care applications and other forms of court work, were a "major issue".
He said work is under way with the Ministry of Justice (MoJ) to "stem demand".
News of the work comes as latest figures show a new record number of care applications for a single month. Figures published today show that in July a total of 1,305 care applications were made - a 2.4 per cent increase on the previous record for a single month in June 2016.
It means that for the first four months of the 2016/17 financial year there have been a total of 4,959 care applications - a 20.4 per cent increase on the 4,118 applications in the same period of 2015/16 - which was itself a record year.
"Work is under way with the MoJ on our future operating models across private and public law, an important part of which is assessing which measures may help stem demand, while ensuring those in need still receive a service," Douglas said.
Douglas described Cafcass's budget for 2016/17 as "manageable", but added it will still be a "stretch target" given the likely level of increases in this year.
"We will have to continue to sharpen our working practices and to innovate to stand still," he said.
"A great deal of my time will continue to be spent on assessing the impact of budget changes, the cost of proposed reform, calculating and identifying potential savings, and factoring in any additional costs from reforms.
"I will also be paying particular attention to whether any of our teams are approaching a tipping point in terms of pressure, which is a known factor to watch out for in child protection work when pressures are high over a long period of time."
Douglas added that he has been in discussion with the president of the Family Division Sir James Munby, senior judges, the Legal Aid Agency and other delivery partners about the potential for bringing cash limited budgeting principles into the family justice system.
This would involve fixed budgets being set for Cafcass services in each local court area and a pricing schedule being created for different types of work, such as a Section 7 report, or monitoring a contact order for a contact.
"This could be a significant development for the years ahead and we will continue to pursue realistic policy options for this," Douglas said.
"My challenge is to continue to deliver efficiencies and be part of future sector transformation, while managing a demand-led service and ensuring we maintain safe standards with incoming cases."