According to a report in the Zimbabwean newspaper, The Independent, Mr Mengistu left the capital, Harare, last December to seek asylum in the hard-line Communist state, a former ally both of Ethiopia and of independence fighters in the southern African country.
After he was ousted in 1991, Mr Mengistu was sheltered in Zimbabwe by President Robert Mugabe, "for his support of the independence struggle". But he had become concerned over his security and Mr Mugabe's political future.
The family of Mr Mengistu, who ruled Ethiopia from 1974 to 1991, are understood to be still in Zimbabwe, but the former despot has spent an increasing amount of time abroad after reportedly moving house in Harare following an alleged assassination attempt.
President Mugabe's position is seen as increasingly tenuous, amid a deepening economic crisis and his unpopular decision to send 10,000 troops to the Democratic Republic of Congo in support of President Laurent Kabila.