The boss of British Airways-owner IAG has called for an end to Heathrow airport's "monopoly" on its terminals.
Willie Walsh claims that allowing third parties to build and run terminals would cut costs for passengers and airlines.
"Most major US airports have terminals owned or leased by airlines. There's absolutely no reason why this cannot happen at Heathrow," Mr Walsh said.
Heathrow said it did not believe such a model was appropriate.
IAG, which owns Iberia and Aer Lingus as well as BA, controls just over half the landing slots at Heathrow – Europe's busiest airport.
Mr Walsh's call is the latest salvo in his ongoing war of words with Heathrow, which is ultimately owned by Spanish firm Ferrovial.
He has long been a vocal critic of the fees imposed on airlines by Heathrow, which stand at about £22 per passenger.
IAG said the proposed expansion of the airport could allow independent companies to build and operate commercial facilities at the airport, including terminals.
"Heathrow's had it too good for too long and the government must confirm the Civil Aviation Authority's powers to introduce this type of competition," Mr Walsh said.
"This would cut costs, diversify funding and ensure developments are completed on time, leading to a win-win for customers."
Last month he wrote in the Financial Times: "For Heathrow's expansion to succeed, there needs to be a relentless focus on controlling costs. But I have no confidence that the CAA is up to the task."
A spokesperson said Heathrow wanted to ensure competition and choice between airlines at the airport: "Expansion will open up opportunities for IAG, easyJet, flybe, Virgin and dozens of international airlines with whom we are working closely to deliver expansion at close to current charges."
The Department for Transport is due to publish final proposals for a third runway at Heathrow in the first half of this year. MPs will then vote on those plans.
Heathrow chief executive John Holland-Kaye is due to give evidence to MPs on the Transport Select Committee on Monday afternoon.
The third runway was due to cost almost £17bn, but Heathrow argued that it could complete the project for £14bn.
Airlines fear that the airport will increase landing charges to help pay for the third runway.
IAG has threatened to call for a price cap on landing charges if they do not fall after the new runway is finished.
"With more passengers and the introduction of internal competition, the airport's charges should go down," Mr Walsh said.
"If they remain at current levels we, along with other airlines, support a price cap to ensure they cannot rise and have written to the Transport Select Committee to highlight this."