An unnamed Burmese embassy official last month announced that Prime Minister Win is at a Singapore hospital for medical treatment.
Irrawaddy, a magazine published by Burmese journalists based in Thailand has reported that General Soe Win may be suffering from leukemia.
The prime minister is known for his role in the bloody crackdown on democracy protesters in Rangoon in 1988.
The United States has also accused General Soe Win of being the mastermind behind the attack on the motorcade of Burmese opposition leader Aung San Suu Kyi near Mandalay in (May) 2003.
An unnamed government source says the prime minister's most likely successor will be Lieutenant-General Thein Sein, who is secretary of the State Peace and Development Council.