The tests are being developed by the Basel-based pharmaceutical company Roche, according to reports in the NZZ am Sonntag and SonntagsZeitung.
It is unclear on which flights the tests, which could cost around €10 (CHF10.80) per passenger, will be trialled, the papers said. Lufthansa said it was looking into various price models, such as including a certain amount in the ticket price.
The requirement to have a negative Covid-19 test when boarding a plane could allow exemptions from entry bans and compulsory quarantine, the papers wrote.
Zurich Airport is also reportedly examining how to integrate such tests into its operations.