Kennison, 40, died in the so called Balcony area at the height above 8,000 meters (26,200 feet) on Friday, Nepal's media reported, citing Asian Trekking managing director Dawa Steven Sherpa.
After the Australian started behaving abnormally at the South Summit, two Sherpa guides brought him to the Balcony, where he collapsed, the report said, adding that his remains were still at the site.
In 2006, Kennison was reportedly heavily injured in a road accident and had to spend years in recovery, having to learn how to walk. The man aimed to raise funds to help people in similar situations, the newspaper said.
The ascent to Mount Everest can be extremely demanding for human body due to changing oxygen levels and pressure on the way to the top and back. There have been ten death incidents on Mount Everest in the last several months, with two people still missing. At least 300 people died climbing the world's highest mount since the beginning of records, with the number ticking up each year. The bodies of about 200 people have never been returned from Mount Everest.