The airline group is understood to be in the latter stages of a pitch for a wide-ranging consumer-focused brief covering the UK and Ireland.
It has already moved the account twice within 18 months, which was prompted by the collapse of The Saltmarsh Partnership in May 2012.
It first turned to Consolidated, which had handled the brief before Saltmarsh, then shifted the work to Red in February.
A source close to the pitch said the brief was worth a low six-figure sum, with a strong focus on digital and an international element.
Highlighting the dual French-Dutch identity of Air France-KLM, they said: "It is about consumer brand building, with a strong focus on the strength of the airline’s network and regional hubs."
In 2012 the airline launched a major restructuring effort to reduce debts of €6.5bn (£5.4bn) to €4.5bn (£3.8bn) by the end of next year.
This October it showed continued signs of recovery, with Q3 operating profit up by nearly a third to €634m (£531m).
However, pointing to a continued challenging environment of weak market growth, as well as fluctuating fuel prices and exchange rates, it pushed back its debt reduction target to 2015.
Air France-KLM had not responded to a request for comment by the time of publication, while Red declined to confirm if it was repitching.