SAS has logged losses for the past four financial quarters amid attempts to restructure its embattled Spanish subsidiary, Spanair.
Lufthansa declined to comment on the alleged breakdown in negotiations and would not confirm that takeover talks had taken place.
"It is Lufthansa policy to never comment on market speculation," explained spokeswoman Claudia Lange to The Local.
SAS was hit hard by the Madrid crash of a Spanair plane in August, which left 154 people dead.
The company posted a third quarter net loss last week of 2 billion kronor ($260 million).