Thomas Enders reportedly told a group of Airbus directors last month he "no longer believed in pursuing the programme" and had begun to prepare for it to be terminated, the paper said.
Lists of engineers to be transferred from the A400M to the development of two other key aircraft, the A380 superjumbo and the A350, have already been drawn up, the newspaper added.
Airbus and its parent group, the European Aeronautic Defence and Space Company (EADS), have been in discussions over cost overruns for several months with seven countries that were to buy the transport plane.
A total of 180 aircraft had been ordered for around €20 billion ($29 billion) but clients are being asked to pony up billions more to cover unexpected costs. The newspaper said Enders estimated the chances of reaching an agreement at around 50-50.
And the German executive "is not ready to threaten the civil aviation division, which is doing well, just for the A400M," a source close to the matter was quoted as saying.
The plane made its maiden flight on December 11 in Spain, but deliveries are at least three years behind schedule.
A spokesman for Airbus said the company had restructured the troubled project in recent months, but there had been no progress on the issue of price. Therefore Airbus had asked European governments to bear a portion of the increased cost.
“We hope the discussions with the nations making the first orders will be finished with a positive result in January,” he said.
And the German Defence Ministry said it aimed to continue with the troubled project.
"We... will continue to clarify the necessary details for a continuation of the programme with the industry until the end of the month," a ministry spokesman said.
He added that state secretaries from the seven countries planning to buy the plane were planning to meet in mid-January.
The A400M is the largest European military project in history. Seven nations – Germany, France, Spain, Britain, Turkey, Belgium and Luxembourg – want to use it as their primary heavy-lift transport. Germany, with 60 planes, is covering the lion's share of the order.