Dover Grammar School for Boys could be demolished and replaced with a new building.
The plan is to put up the new one first, which would be on land in front of the existing structures, and knock down the school's 1930s ones.
This is favoured over the alternative of refurbishing and extending the existing buildings.
The whole project is hoped to be completed by 2022.
Les Craggs, governors' chairman, told the Mercury: "The pupils are using buildings that frankly aren't fit for purpose.
"They no longer meet the standards that current schools would have.
"We are hugely constrained by the the kinds of shabbiness, leakages and asbestos and all the other problems."
Buildings of this age would have had asbestos put in for fireproofing but installing the material has been banned since inhaling the dust was found to cause conditions such as cancer.
Mr Craggs stressed that the material was kept harmless while sealed as at present.
He explained: "It's a phenomenom true of most schools of this age.
"If we were to rebuild or amend some these buildings that's when it would become an issue but it's not an issue at this stage."
Details of these early proposal, from a feasibility study, were shown to the public at an exhibition at the school in Astor Avenue yesterday.
Total replacement would allow for expansion and change in the future and provide a design life of 40 to 60 years.
A new energy efficient building would result in a reduced carbon footprint and lower running and maintenance costs.
The scheme would also lead to improved parking.
Project planners believe that doing nothing is not an option.
The idea is collaboration between the school, the Department for Education and its contractors Kier Construction.
But it is at a very early feasibility stage and the exhibition presented the findings of preliminary work.
Members of the public were able to submit their written comments at the display.
These will help shape the development of a more details scheme and a feasibility report will be written this spring
A decision on whether to go ahead with this idea is expected by early summer and there will be further public consultation.
A planning application will eventually be submitted.
The new school, if built, would be open by summer 2021, with construction beginning next January.
Demolition of the old buildings would be completed by summer 2022 and pupils would first be in the new structure that autumn.
The figure for the cost of the scheme is not known yet.
But it is expected to be funded through the government's Priority Schools Building Programme 2.
DGSB made a successful application for this in 2014
The main building on the site was identified as ‘successful’ in being considered for replacement due it being life expired and in a poor condition.
When the success of the bid was announced, in February 2015, it was revealed that DGSB and Barton Junior were the only two school in Dover district to get this particular funding.