She is believed to be planning to go to Geneva, Switzerland, after the Indian authorities refused her permission to stay in the country for fear of marring relations with the Soviet Union.
She leaves behind a grown-up son and daughter in Moscow.
The American Mutual Radio network broke the news but the American State Department has so far refused to comment.
Since her father's death in 1953, little has been heard of 42-year-old Svetlana Alliluyeva - who prefers to be known by her mother's maiden name.
Svetlana Alliluyeva was allowed to stay in Switzerland for three months. On arrival at New York, she held a press conference and astonished the world by denouncing her father's regime - much to the irritation of the Soviet leader of the time, Alexei Kosygin, who said she was a "sick person".
Later that year, she published her memoirs, Twenty Letters to a Friend, and another autobiography in 1969 called Only One Year.
The tragedy has left Diamantopoulos’ wife and the victim’s twin sister reeling.
Anastasia Koretskaia said she and her twin sister always told each other how lucky they were to have each other.
The twin sister of a 35-year-old woman who was killed in a motorcycle accident near Evergreen Brickworks over the weekend says she does not know how to live without her sibling who she describes as her “gift of life.” Svetlana Koretskaia was killed Saturday night in a motorcycling accident.
Couples in particular like the location – they rated it 10.0 for a two-person trip.
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She returned to the Soviet Union in 1984 and settled in Tbilisi, Georgia - her father's homeland.
In 1986 she left the USSR for the second time to live in the US and then during the 1990s settled in England.