Negotiators said on Tuesday that two-thirds of the parliamentary committee met and examined ways of making "three possible modifications" to the document aimed at satisfying the Sunnis.
Shia MP Abboud Wahid al-Issawi said the first modification concerned Article 3 which stipulates that only the "Arab people" of Iraq are part of the Arab nation, thereby excluding the country's Kurds who are largely autonomous in northern Iraq and speak their own language.
"The amended article will include words stating that Iraq is a founding and active member of the Arab League and respects its charter," he said.
Another change involves Iraq's rich water resources, the control of which has been granted by the draft to the central and regional governments, Issawi said.
The modified text will say that "managing water resources must be done according to international laws and conventions", he said.
The third amendment under discussion concerns how power should be shared between the prime minister and his deputies.
"The amended article will include words stating that Iraq is a founding and active member of the Arab League and respects its charter"
Shia MP Abboud Wahid al-Issawi
Parliamentary Deputy Speaker Hussein Shahristani said an announcement would be made about the constitution on Wednesday morning, and hoped that the draft committee would be able to agree and submit its final document to the United Nations on Wednesday.
The UN is responsible for seeing the document printed and distributed to some five million homes around the country ahead of a referendum expected to be held on 15 October.
If time runs out for distribution to homes, the charter is to be printed in Iraq's newspapers.
Sunni Arab leaders, whose minority community provides the backbone to the ongoing uprising, have accused Shia and Kurdish leaders of seeking to ram the draft through over their objections.
The electoral commission has said that 6000 polling stations would be open on 15 October for the referendum in which 15.5 million registered voters would be asked to say accept or reject the draft text.
General elections are set to take place on 15 December.