The Olympic Delivery Authority is hoping that work on the aquatics centre will begin next July, two months earlier than planned.
Sole bidder Balfour Beatty submitted its tender for the scheme last month and is locked in talks with ODA chiefs amid claims that its initial bid for the job - which includes a 250 m long footbridge - was as high as £250 million.
An early start on the complex would mirror that of the main stadium, the start date for which was brought forward from the middle of next summer to April.
The 10 ha aquatics site is currently the busiest part of the main venues, with Nuttall carrying out land remediation work before piling rigs move in next summer.
Around 500 m of river wall piling has been completed and utilities diversions are being installed.
ODA chief executive David Higgins declined to say how much the budget for the centre is but it will be revealed when Mr Higgins and other ODA officials submit its investment case for the project to the Department for Culture, Media and Sport next week.
Olympics minister Tessa Jowell is expected to make a decision next month on the final cost of the Zaha Hadid-designed scheme, which carried an initial price tag of £75 million.
An ODA spokesman said: "It is important to remember that this is a significant project - not just the construction of a state-of-the-art sports venue but also the construction of a huge bridge, which will form part of the roof, and a significant amount of other work."
The designs for the centre are at RIBA stage D, which involves working up detailed designs, and the ODA is hoping to appoint a preferred contractor by next February.
The price tag for the work is expected to be around £220 million and as well as the centre, will also include the water polo venue and the bridge - which at its widest will be 40 m across.
It will run from Stratford City to the swimming pool complex and it alone is thought to be worth around £90 million.
The entire site now has more than 2,000 workers on it with more than 90 per cent of the site cleaned up. The ODA said that it had not found anything unexpected in the ground.
The only remaining public sites left on the Olympic Park are a bus depot, which will be moved before Christmas, and a travellers camp, which will be relocated early next year.
Analysis: Don't blame the ODA for price guess
By David Rogers
When the ODA reveals the price tag for the aquatics centre, it will get a clobbering. Understandably, it's far happier talking about what a great thing it will be rather than how much more it will cost than it initially thought.
But this is not the ODA's fault. It did not put in the guestimate when it submitted the bid document to the IOC for the 2012 Games. The Government did.
That is looking more than ever like it was worked out on the back of a fag packet, but it is not the ODA's job to worry about what happened back in 2005. It needs to get on with building the venues.
So an early start, once this crucial period of horse trading with Balfour Beatty is successfully completed, would be an ideal fillip - because, for the moment, the news about the aquatics centre is likely to be more negative than positive.