Many of the new political parties in Iraq are all nominating their candidates for judging and prosecuting the ousted president.
However, the Iraqi National Congress (INC), headed by Pentagon-appointed Ahmad Chalabi, appears to have stolen a march on rival parties on Wednesday.
Publicising his own choice for the general director of the tribunal, Chalabi surprised a few by announcing his own nephew - Salim Chalabi.
The INC leader also nominated seven judges and several lawyers to prosecute Saddam Hussein.
The Iraqi National Coalition headed by Adnan Pachachi and the Supreme Council of the Islamic Revolution headed by Ayat Allah Muhammad Baqr Al-Hakim are yet to name their preferences.
The tribunal has been allocated a budget of $75 million for 2004-2005, but did not set a date for the trial of the ousted president.
The court will decide the charges he will face, which could include genocide and crimes against humanity.
Saddam was captured by US troops in December and has since been held by US occupation forces at an undisclosed location.
A spokesman for the Iraqi National Congress (INC), Intifadh Qanbar, announced that Salim Chalabi should be president of the court.
Ahmad Chalabi hopes his nephew
will preside at the court
Chalabi is a US-educated lawyer, but all judges and prosecutors will undergo US training anyway – a programme to include international law, war crimes and crimes against humanity.
Documents seized by American forces since the war are likely to form part of the evidence against the former Iraqi leadership.
US officials claim that since the fall of Saddam, 300,000 bodies have been found buried in mass graves – the former president's Kurdish, Shia and personal adversaries.
But a French lawyer expected to defend Saddam has said a fair trial would be impossible.
Jacques Verges said it was unjust that no formal charges had been presented, so that neither Saddam nor anyone else knew what he was accused of.