The Civil Aviation Authority is expected to decide this week on whether to approve Heathrow’s plan to spend £3.3 billion on planning and early construction of its proposed third runway.
The Times reports the CAA board will meet on Wednesday to discuss the plans.
There have been concerns that costs could be passed on to airlines and passengers through higher service charges before the project receives planning permission, the Times said.
IAG chief executive Willie Walsh said: "With environmental, financial, political and legal hurdles ahead, there’s no guarantee a third runway will ever be built.
"The CAA’s role is to regulate the airport effectively and protect passengers. It’s completely unacceptable for them to expect customers to stump up cash for something that’s not yet got the green light."
Last week, Prime Minister Boris Johnson raised the possibility that the third runaway project could be ditched, telling BBC Radio 5: "Personally, I think that the promoters of the third runway at Heathrow have yet to satisfy the courts, the law, when it comes to our very stringent standards on noise, pollution and air quality."
A spokesman for Heathrow said: "This is a project that will deliver tens of thousands of jobs across the country, connect all of Britain to global growth and will introduce competition between airlines to bring down air fares . . . The CAA must recognise that it is in the consumer and national interest to allow us to deliver Heathrow expansion as quickly as possible."
The CAA declined to comment.
