A spokeswoman said the school would "act as a major language resource, on a greater scale than anywhere else in London, or indeed the country".
The borough was not revealing the full cost of the scheme, but said it would cost Pounds 20 million to buy and remodel the St Mark and St John site in King's Road, Chelsea, which currently belongs to King's College.
The Department for Education appears lukewarm on the proposal and has yet to give the go-ahead. It said: "We are continuing to have discussions with Kensington and Chelsea about this interesting, novel and complex proposal. "
The National Union of Teachers was worried about the borough's proposal to lengthen the school day and year at the new institution, and the effect that a selective school would have on local secondaries.
It says there are already enough selective schools in the area.
But the borough spokeswoman said: "There is little choice available to parents in the south of the borough. Only 75 per cent of parents get their first choice of school - the second worse outcome in the country."