Two schools in Abingdon - Dunmore Infants and Junior - could merge or become part of a bigger Fitzharrys School.
The future of the two schools, in Northcourt Road, is in the melting pot and already the idea mooted by Oxfordshire County Council has met opposition from some parents.
One of the main teachers' unions has said it will "monitor events closely".
The idea is to amalgamate the schools into one or create a school catering for all pupils from the age of four to 19 at Fitzharrys.
Dunmore Junior is currently on special measures.
A paper outlining the options will be issued to parents, governors and staff by November 13. There will also be public meetings on November 21 and 22.
Judith Morris, head of educational effectiveness at Oxfordshire County Council, said: "The junior school faces particular challenges and we want to ensure the best organisation to support the school in its drive to raise standards for all its pupils.
"We hope parents, governors and the wider community will contribute."
Parent Karen Sharp, of Chandlers Close, Peachcroft, said: "I and many other parents are horrified at what's being proposed. It has come out of the blue."
Mrs Sharp, 32, added: "Why mess around with the junior school again when it needs a period of stability?
"The infants is a great success story. The head Linda Konieczny is wonderful. She knows all the children by their first name and puts people before paperwork.
"It's a family school and should be kept as it is."
Another parent, Jayne Lonsdale, from Drayton, said: "I think the county council is viewing this as a money-saving exercise, fewer staff and sale of land."
Brenda Williams, Oxford divisional secretary of the National Union of Teachers, said: "Clearly there could be implications for teachers and staff and of course the children.
"We will be monitoring developments."
Mrs Morris said the county council had no plans to sell off school land.
She said if one of the two consultation options was chosen all staff would be asked to reapply for their jobs but given that pupil numbers would be the same nearly all staff would be needed.
A total of 506 children attend both schools - 265 at the junior and 241 at the infants - and there are 88 teachers and staff.
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