Michael Treichl, 69, who owned Parnham House in Beaminster, Dorset, died "having suffered severe depression", a spokesman, on behalf of his family, said.
The blaze at the family home happened in the early hours of 15 April.
No-one was inside the property at the time, police previously said.
A 68-year-old man, from Beaminster, was arrested on 19 April on suspicion of arson.
Other media reports, including in the Dorset Echo, said the arrested man was Mr Treichl, but police have refused to confirm this.
A spokesman said: "Dorset Police is aware of recent media reports about a death abroad in relation to Parnham House.
"We are awaiting formal confirmation of the details which may take some time.
"Once this has been received, officers will look into whether the investigation will be affected."
The family spokesman said Mr Treichl "enjoyed a long and distinguished career in finance" and added his wife Emma, their two children and his two step-children were "devastated" by his death.
Parnham House was described as "architecturally brilliant" in a 2009 Dorset Life article.
It was home to the Strode family, prominent aristocrats, for about 200 years.
It was later used as a country club and nursing home. In 2001 it was refurbished by a private owner.
Much of the current design was created in 1810 by John Nash, an architect who worked on the 19th Century enlargement of Buckingham Palace.
The owner of a 16th Century stately home that was severely damaged by fire in a suspected arson attack has died.