Christoph Franz, chief executive of Deutsche Lufthansa
Die Welt, citing sources familiar with the situation, said Franz was in talks with the airline's supervisory board about a departure before his contract expires.
Handelsblatt, citing company sources, reported he was now in advanced talks to join Swiss drugmaker Roche
Citing sources from Roche, Handelsblatt also said a decision has not been reached yet but that the talks have reached an advanced stage.
The two newspapers released on Sunday are an advance copy of reports to be published on Monday.
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Asked about the two German newspapers' report, a Lufthansa spokesman declined to comment.
Swiss newspaper NZZ am Sonntag, citing two reliable sources, said 53-year-old Franz is the favourite candidate to replace current Roche chairman Franz Humer, who plans to step down next spring.
Roche's board is scheduled to meet on September 26-27 to elect the next chairman, according to the paper.
A spokesman for Roche declined to comment on the report.
Franz has been a member of Roche's board since 2011. While he lacks a pharmaceutical background, he is a German speaker, and his experience of running a global listed company and his knowledge of Switzerland would be deemed crucial for the role.
But Franz, who has been chief executive officer and chairman at Lufthansa since January 2011, is in the middle of a strategic overhaul at the German airline, which could complicate any departure. His contract is due to expire in March 2014.