Akbar Al Baker, the chief executive of Qatar Airways, told The Financial Times in an interview published on Thursday, that his airline was "on the point of signing" a letter of intent for the purchase of the new jets.
In Moscow, Valery Okulov, Aeroflot chief executive, said that his airline would sign a deal for 22 A350s "in the weeks to come".
Airbus launched the 10-billion-euro A350XWB project last year to rival Boeing in the mid-sized jet segment of the market which the US manufacturer has come to dominate with its 777 and popular new 787 Dreamliner.
News of the orders was a timely expression of confidence in Airbus, the day before tens of thousands of its workers at factories across Europe are due to down tools to protest restructuring and plans to cut 10,000 jobs.
The company has been hit by delays with its A380 superjumbo project, order cancellations and abrupt management changes in the past 12 months. It now faces employee disaffection and a battle with trade unions over cutbacks that management says are urgently needed.
Airbus and its parent EADS unveiled a restructuring plan on February 28, to save $6.6bn by 2010 in response to problems caused by delays in production of the A380 superjumbo jet.
Louis Gallois, Airbus chief executive, has repeatedly stressed the importance of the re-organisation and cutbacks, but he has reassured that Airbus is not driving EADS into a cash crisis.
Al Baker said Qatar Airways, which had already placed two firm orders for the A380, would convert two options for another two A380s into firm orders and was considering raising this figure.
No firm order
The Qatar Airways chief executive said the airline would sign the contract in the middle of 2007, and the newspaper said it might be signed formally at the Paris-Le Bourget air show in June.
The Qatari airline had signed a letter of intent in 2005 to buy 60 A350 airliners before the re-design last year.
It had not converted this into a firm order, which had raised doubts about its commitment to the plane.
Aeroflot had previously looked likely to buy the Boeing 787 instead of the Airbus A350, but it suspended negotiations with the US group at the end of February because of political tensions between Russia and the US.