IAG operates the British Airways, Iberia, Vueling and Aer Lingus airlines, as well as Level, a low cost unit launched last year which flies between Europe and the United States.
IAG already operates 12 A380s, and could be interested in buying more if Airbus improved the pricing, Walsh said, although the airline was not currently negotiating with Airbus.
"The pricing that Airbus has offered in the past is unacceptable to us," Walsh said on the sidelines of a conference hosted by industry body Airlines for Europe.
"We've said very clearly to Airbus if they want to sell A380s they need to be aggressive on pricing and when they work out how to sell the aircraft, knock on our door and we'll talk to them."
Airbus secured the future of the superjumbo when it agreed a deal with airline Emirates in January for up to 36 A380s worth as much as $16 billion at list prices.
For Barcelona-based Level, Walsh said he would need to buy planes to meet a plan to grow the fleet to 30 aircraft by 2022, and would consider a number of different aircraft.
"I think in five years' time, I think there might be opportunities for a different aircraft type," he said, suggesting that Level would not just stick to the A330s it currently operates.
"There are Airbus options with the A330-neo or the A350 and as I said more and more we'll see Boeing 787s becoming available at that stage," Walsh said, noting that 787s may become an option in the coming years, if their price comes down or second-hand planes become available.
Those decisions may fall to Level's new chief executive. Walsh said IAG was in the final stages of interviews to appoint a CEO for Level.
Among Walsh's other concerns is the building of a new runway at Heathrow Airport in London, where IAG's biggest airline British Airways is based.
IAG would be interested in running terminals at Heathrow, Walsh said.
The company already runs a terminal at JFK airport in New York and Walsh cited the example of Munich's terminal 2, run as a joint venture between airline Lufthansa and the airport, as a "good example" of how this can be done.
"Would I like to run Terminal 5? Absolutely," Walsh said when asked about his interest in running parts of Heathrow.
Walsh has long-complained about the cost of a proposed new runway at Heathrow, and a lack of competition at the airport, and has recently called for Britain to allow other operators to build facilities and run terminals at Heathrow.
"We know how to do it (run terminals) and we know the benefit that that can bring so we're open to doing it," he said.
(Sarah Young - Reuters)