The initial $1bn (pounds 650m) order for up to six of the "stretched" 747- 500 and 747-600 range, which can seat up to 600 passengers, is expected to be announced at the Farnborough Air Show, which begins on 2 September.
The customer is likely to be either Cathay Pacific or Singapore Airlines, both of which were launch customers for Boeing's midsize 777 aircraft, which came into service last year.
The order will come at a crucial time for Boeing. Last week Airbus, a consortium of European manufacturers including Deutsche Aerospace, Aerospatiale of France and British Aerospace, won a $900m order from United Airlines for 24 Airbus A319s to replace its ageing fleet of Boeing 737s. Airbus claimed the order gave it a greater market share than Boeing in new orders for the first time in its 20-year history.
Industry analysts estimate that the "super-jumbo" market - planes with more than 400 seats - will carry more than a quarter of all air passenger traffic by 2010. Airbus's planned large aircraft, codenamed the A3XX, could seat up to 800 people, and will cut up to 15 per cent off airlines' costs per passenger.
The cost of developing such a plane from scratch is estimated to be in the region of $10bn. Airbus has not yet fully explained how it will pay for the A3XX. It will not come into service until 2004 - three or four years after the new versions of the 747.
Airbus's current plan is to tap its shareholders for one-third of the money, possibly via a public share offering, and secure a major strategic partner for another third. The rest would come from repayable government loans. But the company has said it will not finalise arrangements until the end of the year.
British Airways, which has been pushing both manufacturers for such large aircraft, is considering converting some of the 30 747-400s it has on order to the larger 747-500s and 600s, but is understood to have been persuaded by Airbus to wait for its more concrete proposals before making a decision.
Recently General Electric and Pratt & Whitney announced they would collaborate on a new engine to power the "super-jumbos", and Rolls-Royce confirmed that it had reached agreement with Boeing to develop a version of its Trent 900 engine to power the 747-500/600. It has been speculated that the General Electric/Pratt & Whitney alliance might co-fund some of the Airbus A3XX development costs in return for an exclusive engine supply arrangement.
A spokesman for Boeing confirmed that the launch customer for the 747- 500/600 would be an Asian airline, but the details of any announcement would be changing right up until the last minute. "The timing of these things is always in the hands of our customers," he said.