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.

Matthew Llewellyn, 27, of Gilfach Goch, Rhondda Cynon Taff, previously admitted failing to stop at an accident and other offences.
Tye Hawkins was left with life-changing injuries after the crash in Mountain Ash, in September 2015.
Merthyr Tydfil Crown Court heard Llewellyn went on to dump the bike and said he was in Scotland at the time.
The court heard Tye was crossing the road with his mother from behind a school bus when he was hit by Llewellyn's 600cc Suzuki motorcycle.
Llewellyn failed to stop and drove 11 miles (18km) away before ditching the bike and hiring a car to get away.
When he was eventually traced two weeks later, he denied any involvement and claimed to have been in Scotland at the time.
The court heard another man was arrested as part of the investigation as a result of the false information he gave police.
He eventually admitted owning the motorcycle but claimed he had sold it, before later admitting his part in the crash.
The court heard Tye suffered a blunt head injury which caused bruising to his brain, along with other fractures and lacerations.
He spent 17 days in intensive care and is preparing to spend three months at a specialist brain injury recovery centre in Surrey, which it is hoped will help him regain movement.
In a victim impact statement, his mother Clair told the court the months since the crash had been "the worst of my life".
"Seeing him struck has haunted me. I have seen changes in Tye, he finds it difficult to concentrate, he hallucinates and needs help to dress," the statement added.
The court was told Llewellyn had written to Tye's family to express his remorse and admitted leaving the scene was "totally reprehensible".
Sentencing Llewellyn, Judge Daniel Williams, said he had showed "no concern for this young lad and every concern for your self preservation".
Llewellyn was sentenced for attempting to pervert the course of justice, driving without insurance and failing to surrender in relation to the crash.
He was also banned from driving for 12 months.
An east London school could become the biggest in the country after being asked if it can take in 2,500 pupils.
[NEXT_CONCEPT]
A motorcyclist who left a 10-year-old boy with brain injuries after a hit-and-run has been jailed for 15 months.