According to reports, paramedics and firemen were called to an area near the royal residence in the early hours of Tuesday morning (9 February) following reports a man had set himself on fire.
He was pronounced dead at the scene.
The Evening Standard reports the first people on the scene were officers stationed at the palace, who tried to help the unidentified man. It's believed he had earlier left a hospital where he'd been admitted for his own well-being.
A Scotland Yard rep said: "Officers in Westminster were called by a central London hospital at 12.06am today after a man in their care had failed to return.
"Police carried out inquiries to trace this missing man at his home address and two associated addresses but the man, aged in his forties, was not present.
"Subsequently, police in Kensington and Chelsea were called to an area near the locked parks of Kensington Palace, W8 at 3.06 am following reports of a man behaving suspiciously. Officers attended and found a man ablaze. At this early stage, no other persons are believed to be involved. This incident is not being treated as suspicious."
Prince William and Kate Middleton, and their children George and Charlotte, split their time between Kensington Palace in London and Anmer Hall in Norfolk. It's thought they were in Norfolk and not London when the incident occurred.