A conflict that threatened to undo a 15-year merger at Europe's largest airline may be unwinding.

KLM Chief Executive Officer Pieter Elbers signed off Friday on a governance plan proposed by Air France-KLM CEO Ben Smith that reinforces cooperation between the airlines without changing their structures, La Tribune reported.

The plan includes appointing Elbers and Air France CEO Anne Rigail as Air France-KLM deputy CEOs and may be presented at Tuesday's Air France-KLM board meeting, according to the French newspaper, which didn't say where it got the information.

A person familiar with the plans, however, told Bloomberg News on Sunday discussions were on the right track to resolve the issue. There is no deal yet, the person said.

Air France-KLM has been facing a revolt from its Dutch arm just as it looks set to turn the page on crippling labor strife at its French entity last year. A tussle over the reappointment of Elbers at KLM sparked a noisy demonstration of support for him Thursday from staffers, managers and even Dutch officials, and a petition signed by more than 25,000 employees.

La Tribune's report suggests Smith is backing off from a prior plan to replace Elbers on the grounds that he might not be fully behind plans to strengthen ties between Air France and KLM. The controversy has brought to the fore long-simmering tensions between the French and Dutch carriers, which joined in a 2004 merger but operate semi-independently.

No decision has yet been taken on appointing an Air France-KLM manager to KLM's supervisory board, according to La Tribune. Still, Air France-KLM Non-Executive President Anne-Marie Couderc, rather than CEO Smith, is an option, it said. An Air France-KLM spokesperson declined to comment to the newspaper.

Air France-KLM reports full-year earnings on Wednesday. After securing an agreement with staff at Air France, Smith needs to complete further steps to pare costs and boost sales if the French unit is to close the profitability gap, not just with European rivals such as British Airways Plc but also with KLM.