Prime Minister Iyad Allawi told Aljazeera on Monday that Hussein and other former officials would also be handed over to the transitional government, with their trials starting "as soon as possible".
"All the current detainees, without exception, will be handed over to the Iraqi authority. The handover will take place within the next two weeks."
The ousted president was captured in December 2003 near his home town of Tikrit. He has been in US custody at an unknown location ever since.
Washington agreed to give him, and other indicted officials in its custody, to Baghdad for trial once a "sovereign" government sets up a special tribunal capable of conducting a fair trial after 30 June.
The tribunal plans to charge some of Saddam's associates by the end of this year, court administrator Salim Chalabi said last week.
It hopes former Saddam aides captured by US occupation troops will also testify against him during their prosecution, which could take many months.
However, a US official cast doubt on the exact date of Saddam's handover.
"The issue of Saddam is something we are discussing. If the Iraqis want him, we're receptive to ideas to transfer him. But I am not aware of any plan that's been worked out on this," a senior State Department official in Washington said.
"Still, if they're going to push on it, we are not going to push back."
Speaking at a press conference later on Monday President Bush would not commit to a date saying that the US would need to be convinced that adequate security measures were in place.
"I want to make sure that when sovereignty is transferred, Saddam Hussein stays in jail," he told reporters.