The council insists there will be no compulsory redundancies.
It said the planned transformation of services was designed to make them more efficient and customer focused.
Savings suggestions include offering more online, having a neighbourhood approach for face-to-face services and reducing voluntary grants by 10%.
Council officials will now consult with staff and unions, insisting the changes will make the organisation leaner and more efficient.
Alasdair Rankin, Edinburgh city council's finance convener, said: "The council needs to take significant steps to tackle the financial challenges it faces as demand for our services continues to increase.
"At the same time, we want to make services for residents more efficient and effective.
"We set the direction of travel last month when council agreed proposals for a new organisational structure, enabling more effective decision making at neighbourhood level and improved partnership working with third sector organisations.
"We are now considering detailed proposals around this and how we plan to improve the way we interact with residents."
He added: "We believe these priority areas for change will enable us to achieve service improvements as well as cost savings.
"Of course change on this scale brings challenges but we need to take decisive action now to meet our targets and create a stronger, leaner, more agile council to better serve the people of Edinburgh."
The latest proposals will be considered by the finance and resources committee next Thursday.
More than 1,200 roles are set to go at Edinburgh City Council over the next three years under proposals to plug a £67m funding gap.