Goldman Sachs, the US investment bank, said it would not proceed with an offer after discussions with the UK company's board came to an end.
The withdrawal should give Spanish infrastructure company Ferrovial a clear run, after it secured the support of BAA for its takeover offer on Tuesday.
Goldman, which is acting as part of a consortium, raised hopes of a further twist in the takeover battle when it said early this morning that talks with BAA directors were continuing.
But that was quashed 20 minutes later as BAA said talks with the Goldman team had ceased.
Ferrovial then tightened its grip on the Heathrow and Gatwick owner by buying a further 12.9 per cent of the company to add to the 15.8 per cent already in its ownership.
Goldman also faced the hurdle of a £115.5 million break fee, which BAA would have to pay Ferrovial if it changed sides.
It was reported that Goldman had put pressure on the Takeover Panel to scrap the fee, as it said it was not in shareholders' best interests.
The fee is equivalent to 10p a share in a bid battle where Goldman's approach is already 5p a share higher than the offer on the table from Ferrovial.
It is thought BAA sided with the Spanish team because its plans for the operator were more advanced.
The successful approach from Ferrovial came in at 935p a share - equivalent to £10.11 billion - but featured a pledge to include a final BAA dividend payment, taking the overall value of the offer to 950.25p, or £10.3 billion.
The Goldman Sachs-led consortium made an offer worth a total of 955.25p, including the dividend.