The Weald of Kent girls' grammar school wants to open an annexe in Sevenoaks.
In a series of letters to Education Secretary Nicky Morgan, the council said a £34m deal had been struck with contractors for a grammar annex and a free school.
However, if the schools cannot be built at the same time, the cost would rise.
The authority told the government it had developed the former Wildernesse School site in Sevenoaks for Trinity Free School and the grammar annex, subject to approval.
But it said the cost of building just one school would be disproportionately higher due to the loss of "economies of scale".
Letters from council leader Paul Carter, councillor Roger Gough and education director Patrick Leeson to the Department for Education (DfE) were released under the Freedom of Information Act following a request by BBC South East Today.
The council said it wanted assurances that any additional costs would be met by the government and not the authority.
In the most recent letter, Mr Carter congratulated Ms Morgan on her reappointment but said there was some "unfinished business in Kent" and an "early decision would be most welcome".
Sarah Shilling, of the Sevenoaks Grammar School Campaign, urged the education secretary to "get on with it and sign it off".
She said: "You can get a free school up and running in a year that caters to a religious minority group, which is what we've got in Sevenoaks, and for a school that selects on, say, being good at maths it's taken three years so far.
"She's got no excuse."
The law forbids the opening of new grammar schools, but changes made by the coalition government in 2012 allow enlargement of existing schools.
The DfE said it was continuing to look into the issue.
A delay to a government decision on whether a grammar school is allowed to expand could cost Kent County Council £4.9m, the authority has claimed.