Diplomats on the 15-nation council said a consensus was emerging about how much authority should be handed over to an Iraqi interim government after a special Sunday session.
Talks were held to discuss a move by France to present some changes to the text. A revised version is due on Monday.
Negroponte said a final version would be in the hands of council members late on Monday evening "with the idea of voting on it on Tuesday afternoon or Tuesday evening."
Ambassador Abd Allah Baali of Algeria, the lone Arab member of the council, said there was "no more real obstacle" to a consensus on the resolution.
France proposed that Iraq has to give its agreement to major operations by US troops in an amendment to a US-British Security Council draft resolution on Baghdad's future.
Letters from Iraq and the US, which will be attached to the resolution, say the two countries had agreed on a framework to coordinate military operations and to seek agreement on sensitive political ventures.
But France proposed an amendment during closed-door consultations that would make explicit the powers of an Iraqi interim government, which takes office on 30 June.
It says Iraq could decide on whether its own forces would engage in a US-led military operation and "that its agreement will be required on sensitive offensive operations."
It was unknown if the French initiative, which its diplomats say is backed by Algeria, Germany and China, will delay adoption of the resolution.