Oxfordshire County Council said two independent studies found having one organisation to run all services could save £100m over five years.
But the plan is opposed by the county's five district councils, who have argued in favour of three councils instead.
All the authorities have been criticised for engaging in a "turf war" over their rival devolution plans.
County council leader Ian Hudspeth said public money should be spent on providing services, rather than running "six separate organisations".
The district councils have argued the county needs an elected mayor, rather than fewer councillors, to get more money from Whitehall.
Oxford City Council leader Bob Price said the county's plan was "the wrong proposal at the wrong time".
He added: "For the people of Oxford, a unitary council would be a disaster.
"The needs of a multi-ethnic and socially mixed urban community are very different to the more rural parts of the county."
Leader of West Oxfordshire District Council James Mills said the aim of the district councils' devolution bid was to get more money from central government.
He said: "A mayor gives a strong voice to Oxford, single point of contact to government and is accountable to the people of Oxfordshire."
But Mr Hudspeth said the proposal was needed because the county council "cannot continue to make savings without further cuts to local services".
He said: "One council for Oxfordshire would be more efficient and simpler for residents, with one phone number, one website and one point of contact."
Residents are being asked for their views before the final proposal is considered by the county council's cabinet on 14 March.
A proposal to abolish six councils and create one county-wide local authority for Oxfordshire has been published.