Barking and Dagenham Council could ask Robert Clack School to expand to a 16-form entry system in an effort to cope with rising pupil numbers.
The borough is one of 11 London councils that face big increases in demand for secondary school places.
The country's biggest post-11 school is currently Ashfield Comprehensive in Nottinghamshire, with 2,492 pupils.
Robert Clack is an oversubscribed mixed comprehensive in Dagenham which specialises in science.
It currently has around 1,900 students.
Barking and Dagenham has experienced the biggest growth in London in the number of children aged up to four.
"By 2020, we will need around 30-35 more forms of entry," said a council spokeswoman.
She said adding just two or three forms could overburden a school, but adding six would allow it to build more classrooms and facilities.
She added: "These proposals are being discussed with schools and no decisions have been taken. This is an option available to more than one school."
A report by London Councils earlier this month predicted London would need an additional 78,000 secondary places by 2020.
According to the report, the cost of creating new school places means the capital faces a Â£1.5bn funding shortfall over the next five years.
Councils must either expand existing schools, build new ones or rely on free schools - which are outside their control - to meet the demand.
The deputy leader of Lambeth Council, Imogen Walker, said it was difficult to plan extra provision.
"With the uncertainty over where free schools are going to open in the borough it is difficult to forecast places available," said Cllr Walker.
"Lambeth's overall projections indicate that there could be some 700 [additional] places required by 2020/21 ."
The London borough of Greenwich is opening three new secondary schools over the next two years to cope with demand.
Hammersmith and Fulham, another borough under pressure, said it was "probably not" planning to create any so-called 'titan' schools.
An east London school could become the biggest in the country after being asked if it can take in 2,500 pupils.