The airport wants to up the fees to help recover losses it accrued during the pandemic, according to the Financial Times.
The UK’s Civil Aviation Authority (CAA), which regulates Heathrow’s charges, is expected to publish its views on the situation next week.
Heathrow, the FT reports, has said it is "in discussions with airlines" over raising its fees, claiming it is the only way it can make up for pandemic-related losses.
But Willie Walsh, Iata director, called on the airport’s shareholders to "step up".
"They have enjoyed steady returns for years," he said. "Instead of expecting the travelling public to be covering excessive returns, it’s time for them to invest."
A Heathrow spokesperson said: "As we emerge from the pandemic, the vast majority of airports right across the UK and the world are having to increase their prices – it’s not a uniquely Heathrow phenomenon, but a legitimate response to keep airports operating and supporting their national and local economies."
"We’ve proposed a balanced increase of 4% to the average airfare which will allow us to continue targeted investment in the airport’s resilience and to maintain basic service standards."