This is the preferred option of the Boston Grammar Schools Federation, which is working to replace the town's current grammars with a single state-of-the-art facility.
Much of the money for the development could be recouped by the sale of the High School site in Spilsby Road, possibly for affordable housing.
However, the new school in South End – which could open as early as 2012 – would only be able to accommodate 1,260 students. The schools currently have 1,344 pupils on their rolls.
"A new school could cost in the region of £20 million, but much of this could be recouped from the sale of the High School site," said chairman of governors Shaun McGarry.
"There are also significant savings in running costs that would enable more of the school's funds to be spent on education, rather than maintaining buildings that are 100 years old and past their best."
Mr McGarry admitted the announcement may come as a surprise to cynics who believed the federation had already made up its mind to keep the High School site after it was revealed the first mixed intake would be at the girls' school.
But the governors always maintained they would wait for the findings of a feasibility study before coming to a final decision.
Mr McGarry said this concluded the majority of teaching spaces at both schools are considered to be undersized and that more than £1.5 million needs to be spent just to bring the current facilities up to scratch.
And after consideration, the federation decided the best option was a move to the Grammar School.
The governors are now working with Lincolnshire County Council to try to secure funding under the Building Schools for the Future programme. The parties expect to find out in March if they have been successful.
"The aim is to build a single state-of-the-art school," said Mr McGarry. "If we have the funding in place, the first tranche of which is now being applied for by Lincolnshire County Council, we could be looking at opening in 2012 or 2013."
As for the reduced intake, Mr McGarry added the number was agreed after reviewing the actual number of students who had passed the 11-plus each year over the last six years, and the current roles in the primary schools.
Mr McGarry said current buildings at the Grammar School site deemed inadequate would be bulldozed, but the listed library and associated buildings would remain untouched.
Head of the federated schools Helen McEvoy told The Standard: "I think everyone regardless of the emotion around the changes, realises that the reality of it is the parents of children who will be coming to the school in the future will want the best possible facilities and opportunities and when you build a brand new school that is what you get.
"This would be absolutely wonderful for the children of the future."
It is still to be decided how the pupils would be accommodated during the construction period.