The outcome of this latest round of talks, which starts in London today and is expected to continue until Friday, could determine whether the US regulatory authorities will give the BA-American partnership their approval. The US government has already stated that it will only approve the alliance if the UK frees up access to Heathrow.
Cyril Murphy, United Airlines' head of international affairs, said the link-up should be approved only if American Airlines gave up the bulk of its lucrative take-off and landing slots at Heathrow.
Stepping up United's lobbying effort, he said this would mean American losing 30 slots at the airport, plus a further six at Chicago and 12 at John F Kennedy airport in New York. These would then be reallocated to other US carriers by the American Department of Transportation.
In addition, BA and American should be prevented from obtaining new slots for five years.
"The price should be paid by the guys who are eliminating the competition, not the guys who are being asked to provide the competition," Mr Murphy said.
The alliance would give BA and American around 60 per cent of seat capacity between the UK and US and give them a monopoly on routes between Heathrow and Boston, Dallas and Miami.
The UK Office of Fair Trading is also thought to have called for the two carriers to divest themselves of slots at Heathrow if the alliance is to escape a lengthy probe by the Monopolies and Mergers Commission.