Savings on Hull's schools rebuilding project are to be given back to central government, the leader of Hull City Council has said.
The Building Schools for the Future scheme envisaged some new builds and refurbishment on eight other schools.
But last week it was announced the government wanted efficiency savings to be found in the scheme.
Council leader Carl Minns said rather than "recycling" savings the cash must go to central government.
He said: "We're not taking any schools out of the scheme, but what we are looking at is how we can make efficiencies out of design and how we work with our builders.
"We're sitting down with our builders and the Local Education Partnership and finding out where we can make those savings."
Mike Whale from the National Union of Teachers said the cuts would have a "terrible impact".
Mr Whale said: "There's a lot of evidence that suggests that new buildings that are in good shape do have an impact on children's learning.
"This (school for the future) has been so hyped and people are so looking forward to it that to have it pulled away at this stage would be quite terrible."
An education spokeswoman at the council said they had written to the headteachers outlining the demand from central government for efficiency savings.
She said there was no specific figure, either monetary or percentage, that had to be achieved, just a suggestion offered to central government of how much money could be given back.
New building work at seven schools should still go ahead because those schemes were already in the planning process.
These were at: Kingswood, Andrew Marvel, Malet Lambert, The Northern Academy, Endyke primary school, Oakfield and a new west Hull primary school.
But schools earmarked for work in the next phase of the scheme could be subject to changes such as refurbishment rather than rebuilding.
These included Hull Trinity House, St Mary's College, Newland School for Girls, some special schools and pupil referral units already scheduled for refurbishment only.