BAA expects to raise £2bn from higher charges, roughly half the cost of the new runway due to be ready in 2011.
Low-cost airlines Easyjet and Ryanair, the airport's biggest operators, are opposed to any increase in duty.
Work on Stansted's new runway is a key part of the government's plans to expand UK airports revealed on Tuesday.
BAA cannot impose any large rises in airport charges, however, for the next five years.
This is because the Civil Aviation Authority, not BAA, sets the fee - and in April this year it was capped for the next five years.
The maximum charge that can be levied this year is £4.89, increasing in line with inflation each year for the next five years.
But, according to BAA the average fee charge it imposes is much less than this, at £2.89 per passenger trip.
Stansted users are also unlikely to have the cost of improving other airports passed onto them in the short-term.
Historical airport charges*
1992-93: £1.13 (actual charge incurred)
1997-1998: £3.16 (actual charge incurred)
Stansted only. Source: BAA
Under the current rules, BAA, which also runs Gatwick and Heathrow, cannot cross-subsidise its airports.
The news comes as a French court barred airline Ryanair from receiving subsidies from the Strasbourg Chamber of Commerce for its Stansted to Strasbourg service.
Each airline ticket is made up of a whole series of components, ranging from fuel costs, baggage handling fees to administration costs.
The airport charge is just one element.
It is not a tax on passengers, but a charge imposed on airlines.
Ultimately, though, it will be passed onto the consumer through their ticket price.
In the last few years, other charges have been passed onto passengers with minimal fuss.
An estimated 124 airlines worldwide have begun imposing a small security and insurance surcharge.
Although there could be a threat of higher airfares in the long-term, the government said that costs to air passengers would rise much faster if extra runways were not built.
If no new runways are provided, it has said, passengers at all the major London airports would face large fare increases by 2030, averaging £100 per return journey, at today's prices.