The Arabic news channels, Al-Arabiyah and Al-Furat, are reporting that Hussein's half-brother, former intelligence chief Barzan Ibrahim al-Tikriti, and Awad Hamad al-Bandar, the former chief justice of the Revolutionary Court, will be hanged on January 4.
The Associated Press and AFP quoted an anonymous government official as confirming this, but that the exact place and time have not been set.
However, a senior aide to Prime Minister Nuri al-Maliki, Sami al-Askari, said no date had yet been fixed for the executions. He said the two would likely be hanged next week.
Ibrahim and al-Bandar were found guilty along with Hussein last year of killing 148 Shi'a from the town of Al-Dujayl following an assassination attempt on the former Iraqi leader in the 1980s.
(compiled from agency reports)