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.

Ray Dare died when his bike and a van were involved in a collision on the A41 Ashton Clinton bypass, near Aylesbury, Buckinghamshire, at about 14:45 BST on Wednesday.
He had belonged to the Surrey-based Kingston Phoenix Road Club for more than 60 years.
A statement on the club's website expressed "huge sadness and shock".
It said Mr Dare had been "attempting to set a new national record for a 91-year-old".
A post on the Timetrialling Forum said: "Other riders have spoken of him riding well and steadily before.
"As yet there are no further details but police, of course, are conducting a fatal accident investigation.
"I am sure all riders will be as shocked as the officials were at this news."
Circumstances surrounding the crash are being investigated and Thames Valley Police is appealing for witnesses to come forward.
The driver of the van was uninjured. No arrests have been made.

The five-storey Bursledon Windmill had its wind shaft and sails replaced following a £94,000 Heritage Lottery Fund (HLF) grant.
Built in 1814, it is believed to be the only working windmill in England that retains a wooden shaft.
Miller Jonathan Cook said it was "long-lived technology that works as well as when it was invented".
It is hoped the windmill will produce its own flour again by summer 2015.
Mr Cook said: "These are important buildings, any opportunity to see a windmill restored to a working condition is great news"
The Grade II-listed structure was rescued by Hampshire Buildings Preservation Trust in the 1970s.
Annabel Cook of Hampshire Cultural Trust, which runs the windmill, said such mills were "a revolution in the way food production was carried out".
"We're hoping to bring to life what the idea of windmilling was and its importance in people's lives," she added.
The HLF funding for the latest restoration project was secured by Hampshire county, Eastleigh borough and Bursledon parish councils, as well as Hampshire Buildings Preservation Trust.
A further £47,000 came from local councils to recruit and train more volunteers in traditional milling skills and help to run guided tours, workshops and special events.
The original timber wind shaft, which drives all the mill machinery and turns the sails, is expected to become an exhibit in an on-site museum.
The building is believed to be one of 27 such windmills regularly working in Britain.
A proposal to abolish six councils and create one county-wide local authority for Oxfordshire has been published.
[NEXT_CONCEPT]
A 91-year-old cyclist killed on a dual carriageway was doing a time trial to set a new national record for his age.
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A 200-year-old windmill in Hampshire has reopened following a two-year restoration project.