Hazim Shaalan made the remarks to the London-based Arabic newspaper Al-Sharq Al-Awsat on Tuesday.
Pressed on whether Saddam's trial would open before Iraqi elections scheduled for 30 January, the minister said: "Yes, before the elections."
The remarks contradict a statement by a US official in Baghdad in September that Saddam, who is currently in US custody in Iraq, is unlikely to go on trial before the end of the year.
The official said 21 investigative judges were working on different issues, and that more time was needed to prepare the prosecution of former Iraqi officials charged with multiple crimes.
He also said the deteriorating security situation in Iraq was impeding the collection of evidence - for instance making exhumations in parts of the country almost impossible.
Saddam, who held power for nearly 25 years, faces seven charges encompassing war crimes and crimes against humanity.
He will be accused of the Anfal "ethnic cleansing" campaign against the Kurds, the gassing of Kurds in Halabja in 1988, the invasion of Kuwait in 1990, and the crushing of Kurdish and Shia rebellions after the 1991 Gulf war.
Saddam has been in US custody
since December 2003
Saddam will also be accused of killing political activists over 30 years, massacring members of the Kurdish Barzani tribe in 1983, and killing religious leaders in 1974.
The former president is unlikely to recognise the authority of the court that will try him, and will argue that it is an illegitimate organ of the occupation forces.
He is also likely to deny all the charges against him or argue his actions were a legitimate response to threats against his government or Iraq itself.