The firm is expected to put in its bid for the project at the end of this month.
ODA chief executive David Higgins said: “We do expect them to submit a bid but if they don’t, we have a plan B. But they are a world-class company and they are very interested in the project.”
Rivals Hochtief and Eiffel have both pulled out over the past few weeks.
Mr Higgins said: “In an ideal world we’d prefer them to be both there, but we would have got to the stage we are now with one bidder.”
He declined to say if the ODA was continuing discussions with other major contractors
as part of its plan but said: “Balfour Beatty is eminently capable of doing the job but the main issue will be the supply chain.”
As well as the aquatic centre, Balfour Beatty is also eyeing up a 250 m long footbridge that will run from Stratford City to the swimming pool complex and is being included in the deal. Mr Higgins said the water polo venue is likely to be tacked on as well.
He declined to put a figure on how much the deal will cost - £150 million is the latest estimate - but he said the ODA will submit its investment case for the project to the Department for Culture, Media and Sport on December 13.
Olympics minister Tessa Jowell is expected to announce a decision in January and the ODA hopes to sign a deal early next year.
Construction work will begin in the third quarter of 2008.
How the other big jobs are faring
Along with the main stadium and the aquatics centre, the other permanent structures will be the media centre and the velodrome.
The media centre will be awarded by the middle of next month. The 1.3 million sq ft site will be turned into a mixed-use development after the Games.
Three firms are left in the race. The Rosemound team – which includes Norwest Holst – is no longer on the list.
Bids are with the ODA from teams featuring Carillion, Balfour Beatty and Bouygues.
Six firms – Alfred McAlpine, Carillion, FCC, ISG, Shepherd and Wates – are working up bids for the 6,000 seat velodrome.