Norfolk County Council, which has already reduced its budget by £334m over the last six years, said a further £125m of cuts across all services will be needed by 2021.
Measures being considered include merging children's services, libraries and other services into the same buildings, with unused buildings and land being sold or leased to generate more income.
In addition, the council is looking to reduce its children in care bill through a focus on early intervention, including therapeutic support for families where a child is at risk of being taken into care.
Last month it announced plans to invest an extra £12m in children's social care in a bid to reduce the number of children coming into care.
"I believe in making the best use we can of the money we have," said council leader Cliff Jordan.
"We're going to look at things like having children's centres and libraries and other services that could fit together well, based in the same buildings. Think about it - that's better for the public and will save money. But it's early days and we're gathering the evidence and talking to people first.
"I think we can save £125m - we're on track this year and next and our future plans should deliver the rest."
Other measures being considered are to improve signposting of advice and support services and move more of its services online. It also plans to raise its council tax by 1.9 per cent.
The plans will be considered at committee meetings taking place throughout October.
Children's services in Norfolk are currently rated as "inadequate" - after the council received the lowest Ofsted rating for the second time in two years in October 2015.
This month Sarah Tough is due to join Norfolk as director of children's services (DSC), taking over from interim DCS Matt Dunkley, becoming the council's sixth DCS in four years.