Television stations have reported that Barzan Ibrahim al-Tikriti, Saddam's half brother and a former intelligence chief, and Awad Hamed al-Bandar, the former chief justice of the Revolutionary Court, will be hanged at dawn on Thursday.
Saddam was hanged on Saturday, the first day of the Eid al-Adha holiday, just four days after the failure of their appeal.
Wednesday is the last day of the religious holiday for Shias in Iraq, but the government has declared a public holiday lasting until Saturday.
Before Saddam's hanging, there were conflicting reports about when it would happen and the government took the final decision only a few hours before the execution.
No second term
Nuri al-Maliki, now under heavy criticism for his handling of Saddam's execution, has said he has no interest in a second term and wished he could be done before the end of his current term.
|Nuri al-Maliki will not seek a second term |
of office [AP]
Al Jazeera correspondent Hoda Abd al-Hamid reported that a mobile phone video of Saddam's hanging has caused the Iraqi prime minister much more trouble than was expected.
"There have been many calls within his coalition to change the prime ministry and to form a new government. He now has to make more effort to bring the Sunnis back into the power structure especially after the leaked video and he has to explain to Iraqis why the video was leaked."
Some supporters of the execution said that the video was released with the intention of creating greater sectarian divides in the country and there are rumours of some people within his coalition trying to form another government.
Asked whether he would accept a second term, Maliki said in an interview published on Tuesday by the Wall Street Journal: "Impossible."
"I didn't want to take this position. I only agreed because I thought it would serve the national interest, and I will not accept it again."
His term is intended to be four years, but it could be cut short by a power shift in parliament.