The company, its main US rivals, UPS and DHL, and Australia's TNT, are currently barred from "fifth freedom" rights which would allow them to carry cargo from the UK to third countries.
Fearing that the freight issue will take a back seat in the talks, or be used as a bargaining chip, FedEx is lobbying other government departments, notably the Department of Trade and Industry.
It claims that BAA, the privatised airports authority which would gain from any increase in traffic, also supports such a move.
FedEx's central argument is that protecting the UK's air cargo market from foreign competitors is only hurting British exporters. "The current rules on express freight are protectionist, but Britain doesn't have an industry to protect," said a spokesman for the company.
While the UK has a thriving international air passenger industry, led by British Airways, the courier business is largely domestic, relying mostly on foreign companies to forward international packages.
As a result, shipments from Britain to India, Japan and Australia often end up taking a scenic tour through the US before arriving at their destination.
A report by the transportation consultancy Portland Group, which was commissioned by FedEx and included in its latest submission, estimates that exports to Asia would rise by pounds 3.1bn a year if the company's request was granted.
Open skies, page 3