In a letter to Scandinavian colleagues, Klevan describes a safety culture characterized by an unwillingness to admit mistakes and a reluctance to cooperate with the authorities, reports Denmark's Jyllands-Posten.
"SAS has gone from being a robust and stable airline to being a decrepit and vulnerable airline," Klevan writes.
"With the way this culture is developing, with the lack of leadership (and a lack of knowledge in vital areas), it is unfortunately just a matter of time, if this continues, before something serious happens."
The document was written in March after Klevan's investigation into a number of incidents in which SAS passengers were exposed to danger.
In one example, SAS allowed a plane to fly even though the captain had seen fuel escaping from one of the wings. On another occasion, 244 passengers' lives were put at risk when their plane's undercarriage hit the runway. In a third incident a pilot allowed a flight to take off despite noticing that an oxygen container was unsealed.
Speaking to Jyllands-Posten, Klevan said he stood by what he wrote.
"This is a tendency that we have observed. It is, as I said, probably just a matter of time before a serious accident occurs at SAS."
SAS deputy chief executive, John Dueholm, rejected the accusations in the report.
"We strongly refute Klevan's comment that SAS has a general safety problem. We have the word of the authorities that flight safety at SAS is in order," he told Jyllands-Posten.