Heathrow says expansion of the airport is "essential", after experiencing its busiest May on record.
More than 7.2 million passengers travelled through its four terminals last month, up 0.4% from a year ago.
A Heathrow spokesperson said: "As these record numbers become the norm, it's time to start an honest conversation about the challenges this presents for an already space-constrained yet highly efficient hub."
Opponents of the west London airport's expansion say increasing air travel would make it much harder for the UK to meet its climate change commitments. The Mayor of London, Sir Sadiq Khan, opposes a third runway at Heathrow for this reason as well as because of noise and air pollution.
Heathrow's spokesperson said: "Heathrow continues to deliver excellent service, but to sustain this performance and meet future demand, expanding capacity will be essential."
The airport has previously said it will submit detailed plans for building a third runway to the government in the summer.
Chancellor Rachel Reeves used a speech on growth in January to give her support to the project, which has been repeatedly delayed over several decades because of environmental concerns.
