An extension for a new music and drama annex at Kings' School, Winchester, has received the provisional backing of the county council.
However, it wants to see more cash pledged by the school itself.
Kings has committed £320,000 to the project but the council says the full cost of connecting services is not yet known and it is likely that the school may need to contribute further funding.
"A contract will not be let until all detailed costs are known and the school has confirmed its contribution," said a spokesman.
Head teacher of Kings', Ray Bradbury, said he hoped a contractor would be appointed by Christmas.
"It's taken a long time to save for the new facilities and we're very excited," he added.
Building work is scheduled to start in January and will be concluded in August.
Council executive member for education, Don Allen, said: "We've talked with the building panel: they are happy with it and I have no problems at all."
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