Sleep apnoea results in breathing being repeatedly interrupted during sleep and is often accompanied by heavy snoring.
Dr Ricardo Osorio, from New York University School of Medicine, who led the new research, said: "We know that about 10 to 20 per cent of middle-aged adults in the United States have SDB and that the number jumps dramatically in those over the age of 65.
"We don't know why it becomes so prevalent but one factor may be that some of these patients are in the earliest pre-clinical stages of AD (Alzheimer's disease)."
A group of 68 men and women with an average age of 71 and no evidence of dementia took part in the study.
Around half (48.5 per cent) were found to have mild SDB and a quarter had moderate-to-severe SDB.
The volunteers had spinal fluid tests and brain scans to identify any early biochemical signs of Alzheimer's disease.
Alzheimer's biomarkers were only found among lean participants with SDB. In these patients, a progressive association was seen between the severity of SDB and the level of two indicators based on proteins and brain scans.
Lean patients with SDB also tended to have a smaller hippocampus - a part of the brain crucial to memory - than other participants.
The findings were presented on Sunday at the American Thoracic Society 2013 annual conference in Philadelphia.
Dr Osorio said it was not clear which condition came first, SDB or Alzheimer's.
"It's really a chicken and egg story," he said.
"Our study did not determine the direction of causality, and, in fact, didn't uncover a significant association between the two, until we broke out the data on lean and obese patients."
His team now plans to test a theory that brain damage caused by very early stage Alzheimer's can trigger SDB in lean individuals who would otherwise not be affected by the condition. Obesity is, by itself, a risk factor for breathing problems during sleep.
After an initial assessment, patients will be given continuous positive airway pressure treatment for sleep apnoea. After six months, they will be evaluated again for biomarker evidence of Alzheimer's.
- PAA