Airport operator BAA is the only organisation in Edinburgh that has "permitted development" (PD) rights, meaning that it does not need planning consent before carrying out development on its grounds.
That means that the council is unable to force the company to spend money on infrastructure improvements or public transport in the way that it can with other developers through "section 75" legal agreements.
Concern has been growing about the council's inability to control what happens at the airport in light of BAA's controversial 1 "kiss and fly" charge.
Dave Anderson, the council's director of city development, is now urging the Scottish Government to abolish the airport's exemption from the normal planning process.
The move came after concerns were raised by Liberal Democrat councillor Charles Dundas and Labour councillor Lesley Hinds, both members of the city's planning committee.
Cllr Hinds said: "This issue came about because of the drop-off charge and people began to question why BAA were not considered the same as everyone else in the city.
"They should be treated the same and should be contributing to the infrastructure of the city if they need to expand."
The reason airports have PD rights dates back to the days when they were state-owned and it was not seen as necessary to have the same controls that were placed on a private firm.
The then Scottish Executive pledged in 2005 to review PD rights, including at airports.
In a new council report, Mr Anderson said: "It is proposed that the council should encourage Scottish ministers to follow through their 2005 commitment and review airport PD rights as quickly as possible."
Bosses at Edinburgh Airport said removing its PD rights would make it "far less competitive" against European rivals and could even lead to them halting any plans to invest.
The company has voluntarily contributed 560,000 towards developing public transport links with the city centre since 2007 and it intends to spend another 250,000 in 2011.
An airport spokesman said: "Should further betterment of our facilities require us to pay development tax and go through the red tape and process of the planning system, we would have to consider these voluntary payments and indeed the viability of these future schemes. "This could stifle Edinburgh Airport."
A Scottish Government spokesman said: "We will be publishing a consultation paper next year and would welcome all contributions to the debate."