BAA is in pole position to take over the running of Budapest airport after making the highest bid for the firm which owns Hungary's largest airport.
More passengers are passing through Budapest airport
The British airports operator has made a £1.2bn (1.8bn euros) offer to buy a 75% stake in Ferihegy airport, which the government is privatising.
Pending the succesful conclusion of negotiations, BAA is expected to sign a formal contract in the next few days.
The privatisation is the largest in Hungarian history.
As well as gaining a controlling interest in the business, the successful bidder will secure a 75-year licence to run the airport.
The Hungarian government said on Thursday that BAA had outbid two other consortia headed by German companies Hochtief and Fraport.
"BAA's offer achieved the highest score, in terms of both the bid's evaluation and the price offered," finance minister Janos Veres said.
The airport is being sold to help finance its future development.
The number of passengers using the airport is rising sharply, boosted by the growth in budget airlines over the past 18 months.
Almost seven million passengers used the airport in the past 10 months, 27% higher than over the same period last year.
Budget airlines have flocked to the airport since Hungary joined the EU in May 2004.
BAA - which operates London's Heathrow and Gatwick airports among others - said it was "cautiously optimistic" it would complete the deal shortly.
The successful bidder will have to upgrade the airport
"We are glad that we are top of the tree both in financial and technical aspects," a company spokesman said of the bid.
"We are looking forward to addressing the main issues and going forward and sealing the deal."
BAA's share price fell after the news emerged, closing down 0.5% at 646.50 pence.
There are concerns that the deal - likely to be funded by BAA taking on additional debt - could constrain the company financially.
As well as the purchase price, the successful bidder will be obliged to invest £265m in upgrading the airport.
Should talks with BAA break down, the Hungarian authorities will turn to the Hochtief-led consortium, which was the second highest bidder.