BAA officials fear this could add substantially to the costs of airport construction projects, such as the £3.7bn Terminal 5 scheme.
Building revealed last week that construction deliveries on the T5 project would occur every 37 seconds during two specific periods of the day.
A BAA insider said that contractors would have to pay through the nose for deliveries unless an agreement with Livingstone was reached.
He said: "As part of talks with the mayor's office we need to discuss whether charges would include construction vehicles and how the scheme would be feasible."
A BAA spokesperson confirmed that officials are seeking a meeting with representatives of the mayor's office.
"We are seeking a meeting to discuss the expansion proposals and until we have clarity on what the wider implications will be for Heathrow as a whole, as well as just T5, we cannot say any more," said the spokesperson.
The London mayor's office said it had no firm plans to extend the charge to Heathrow but Livingstone had expressed an interest in the idea.
A spokesperson said: "Ken has not announced it is going ahead and no feasibility work has been carried out – but we cannot deny it is something he is looking at doing."
In a separate development, it has emerged that contractors are being penalised for reducing the number of vehicles in their fleets in an effort to cut their congestion charge bills.
A letter from Transport for London sent to a leading contractor this month said because it had fewer than 25 lorries, it was no longer entitled to a discount on the charge. The firm lobbied TfL and it eventually reversed the decision.
Strategic forum chairman Peter Rogers said that TfL needed to stop penalising contractors for streamlining their operations and instead reward them for cutting congestion.
Speedy Hire said it had 800 vehicles entering the capital and the congestion charge would cost it an extra £100,000 a year.