"We do not have the kind of willingness to lose as much money as I think whoever buys this company will lose. We just decided to back off and see what other opportunities would arise from time to time in France," said Jonathan Ornstein, chief executive of Virgin Express.
BA, in partnership with Banque Rivaud of France, has been the leading contender in the race to acquire Air Liberte since announcing in October it planned to give Air Liberte a FFr630m (pounds 73m) capital injection.
Mr Ornstein had said earlier he planned to top the bid by BA. "There are other opportunities we are looking at in France," he added.
Air Liberte, founded in 1988, lost FFr650m in the first nine months of 1996 due to a fare war and poor passenger numbers at the airline in the run-up to full liberalisation of French airspace.
BA's offer has to be approved by the creditors of Air Liberte, which has gone into administration.
Mr Ornstein, who believed BA would remain the only bidder, said Air Liberte had a negative operating margin of almost 40 per cent, making any investment "tough".
He added: "In the airline business if you have an operating margin of 8 per cent you're basically under water. I don't know who else could afford to buy them. It's an expensive purchase."
He said he was not criticising BA's purchase of Air Liberte, as they had a very long-term strategic view. "It's just a question of what is the long-term view and where do you want to be 10 years from now," he said.
"These guys have a tremendous dominant position at Heathrow that literally allows them to print money. That can allow you to basically go to places like this and absorb huge losses while you sort of run the other guy dry."
The BA joint plan with Rivaud aims to get Air Liberte back to break-even in 1999. The plan will safeguard 1,250 out of 1,400 jobs at the carrier. BA would get a 70 per cent stake and Rivaud 30 per cent.
Both companies are also paying the costs of running Air Liberte during administration, estimated at FFr150m.