Police said his cause of death would be determined by an autopsy but they warned the process could take months.
The Sun reported a close family source has described the death as a mystery.
“The phrase ‘suspicious circumstances’ has been used but we just don’t know yet,” they said.
Griffiths co-founded Asos, short for As Seen On Screen, in 2000 with his business partners Nick Robertson and Andrew Regan.
The venture has grown into a multibillion-dollar enterprise with figures such as Michelle Obama and Catherine, Princess of Wales seen wearing Asos garments.
Griffiths left the business in 2005 but made millions of dollars in shares sales, including a windfall of about $33 million in 2010.
He moved to Thailand after the breakdown of his first marriage in 2007.
He later married a Thai woman, with whom he had a son and daughter, though they reportedly split in recent years, according to The Sun.
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