"Unannounced checks" could be a "possible means" to ascertain whether pilots were regularly taking anti-depressives, which could provide an indication of potential psychological problems, CEO Carsten Spohr told the daily Frankfurter Allgemeine Zeitung.
The surprise nature of the tests would be similar to the doping tests conducted in professional sport, the newspaper suggested.
Spohr insisted, however, that the airline would have to examine very closely "under which conditions and in what exceptional circumstances doctors might have to be exempted from medical confidentiality obligations."
The group would "submit a corresponding proposal to the 'taskforce'" or group of experts set up by the German government and the airline sector in the wake of the March crash to investigate how to improve air safety, he said.
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Any substance that could impair a pilot's ability to fly a plane, such as medicines, drugs and alcohol, would be covered by the tests, he said.
A jet operated by Germanwings, the low-cost subsidiary of Lufthansa, crashed in the French Alps on March 24, killing all 150 people on board in an apparent deliberate act by the co-pilot with a history of depression.
"But of course we are continually working on minimising the risks of flying still further."
Spohr said that the image of the Germanwings and Lufthansa brands had not appeared to have suffered greatly by the disaster.
In fact, "passengers' trust in us actually appears to have increased," he said.