The company is reviewing its longstanding relationship with incumbent Burson-Marsteller for the six-figure, three-year brief.
The review takes place as the airline undergoes cuts to cope with rising fuel costs and increasing competition from low-cost airlines and Middle Eastern carriers.
These include plans announced last year to cut 3,500 jobs in an effort to quadruple operating profit to just over €2.3bn (£1.93bn) by 2015.
A spokesman for Lufthansa described the process as "part of a regular check-up", and said the winning agency would mostly support consumer-facing work on key markets across the continent.
These include Italy, France, Spain, Russia, Poland and Scandinavia, with UK work continuing to be handled in-house.
Burson-Marsteller, which retained the account after a review in 2010 and has worked for the airline for more than seven years, is understood to be repitching.
In May, Barbara Schädler was named head of corporate comms, moving from business management software firm SAP.
Yesterday, the company announced the unexpected departure of CEO Christoph Franz for pharmaceutical company Roche.