BA wants to buy up to 50 new short-haul aircraft worth about pounds 2.5bn to replace its 757 fleet on shuttle routes in Britain and to European destinations such as Frankfurt, Rome and Paris.
If the deal went ahead, Airbus would take the old Boeings off BA's hands in part exchange for a new order from Airbus.
BA has invited Boeing, Airbus and British Aerospace to bid and has told Rolls-Royce, General Electric and Pratt & Whitney that they will be competing to power the new aircraft.
Airbus, in which British Aerospace has a 20 per cent stake, is offering its recently launched A318 jet, a 107-seat aircraft designed for short and medium-haul use. A part-exchange offer would be seen as retaliation for a deal by arch-rival Boeing to buy 17 Airbus A340 aircraft from Singapore Airlines.
The deal, which outraged Airbus executives, was a key element of efforts to get the Asian airline to convert options for 10 Boeing 777 twinjets into orders worth $1.9bn.
Airbus confirmed it was actively seeking to sell more aircraft to BA but declined to comment on speculation that it will buy back the Boeing 757 fleet on part-exchange terms.
A spokesman for Airbus said: "Of course we are competing in any deal where we think we have the right plane." But he said it was not the company's policy to comment on ongoing discussions. Airbus has previously said it is not in the business of buying aircraft from the competition, although it does occasionally help airlines to re-market older aircraft.
Boeing's 757 carries about 195 passengers on domestic flights and 150 on European journeys. The new order is part of BA's continuing policy to maximise profit on each flight by cutting the number of economy seats and increasing profit from Club Europe business cabins.
Last year BA struck a pounds 5.5bn deal with Airbus for 59 firm orders and 129 options for A319, A320 and A321 aircraft, breaking from its previous policy of buying aircraft only from Seattle-based Boeing .