The Doha-based airline, which surprised the last air show in 2003 at Le Bourget, near Paris, with an order for 32 Airbus planes, is negotiating with the European aerospace giant and its US rival, Boeing, a "new order of some 60 aeroplanes".
"The deal will comprise either the new Boeing 787 or Airbus's A350, or both," depending on the final outcome of the negotiations, an aviation industry source said on Wednesday, requesting anonymity.
"Negotiations with Boeing and Airbus have reached an advanced stage," he added.
Boeing Vice-President John Feren had announced in November that the US aerospace giant was in negotiations to supply Qatar Airways with the long-haul airliner 7E7 Dreamliner, which was given its 787 designation in January 2005.
Clinching a deal with Qatar's flag-carrier would be a first for Boeing, as European manufacturer Airbus aircraft make up the Gulf airline's entire fleet.
Qatar Airways lays claim to be one of the world's fastest-growing airlines, operating a fleet of 40 aircraft from its Doha hub. Founded in 1994, it is owned equally by Qatar's government and private investors.