Wilson's School in Wallington is planning to permit girls for the first time in 400 years.
The prestigious boys' grammar today announced it was to consult with parents, staff and students on a proposal to both expand and become co-educational.
The move comes after all secondary schools in the Sutton area were asked to consider whether they would be willing to expand to meet the expected growth in the number of pupils already entering the borough's primary schools.
A statement released by governors said: "Wilson's wishes to respond to that challenge and has considered carefully what kind of expansion would be best, not only for the school, but also for the community.
"Parents and children in the area are fortunate in having access to a wide range of excellent schools, both selective and comprehensive. Currently, however, they do not have the choice of a selective, co-educational school."
It continued: "We believe that parents will be delighted to have this choice added to the range already available to them. We know that many parents and students prefer co-education and this will provide parents, for the first time, with the opportunity to send their sons and daughters to the same selective school."
Under the plans the school, whose old boys include Michael Caine, will expand from five to six forms of entry and become fully co-educational in Year 7 and the sixth form from September 2015.
If the proposal is backed by parents, staff and students the school said it would consult more widely with the community.
The governors' statement added: "Wilson's School will be celebrating its 400th anniversary in September 2015. As a school with a long history, we are used to taking the long view, as the Governors did when they took the decision to move from Camberwell to Sutton in 1975 to secure the school's future. As we enter the next 400 years of our history, we want to consider how the school can best serve the generations to come and fulfil our Founder Edward Wilson's vision of an education for all. We have come to the conclusion that if Edward Wilson were founding his school today, he would almost certainly found a co-educational school."
