Sponsors of the resolution - the United States, Britain, Argentina and Oman - wanted the measure adopted last night and the Council President, Karel Kovanda, said he was working hard to meet the deadline. A similar resolution has been on the books since 1991 but Iraq rejected it.
The new measure raises the amount of oil Baghdad may sell and eases UN monitoring of the distribution of humanitarian supplies.
This time Iraq's deputy prime minister, Tareq Aziz, is actively negotiating with the sponsors, mainly through Argentina's ambassador, Emilio Cardenas. Mr Aziz has said little but Mr Cardenas told reporters he thought Iraq's attitude was "a bit more positive".
Joe Sills, the UN chief spokesman, said there was "more hope on this not just being approved by the council but being acceptable to Iraq. But I am not making a prediction."
Mr Cardenas estimated the oil sales proceeds available to Iraq would be close to $650m out of each $1bn. A 30 per cent deduction, $300m of every $1bn, would be earmarked for a Gulf War reparations fund and another $50m would go to meet other UN costs.
France and Russia argue that there is no point in adopting the resolution unless it is acceptable to the Iraqis. If it is not, they say, it will turn into a public relations tool enabling the US and Britain to continue blaming Iraq for hardships caused by sanctions imposed when Baghdad's troops invaded Kuwait in August 1990.
Iraq is still reported to be concerned that acceptance of this deal might be a substitute for a complete lifting of the embargo.
France and Russia, backed by China, Indonesia and possibly other states, had wanted sanctions on oil exports lifted entirely once Rolf Ekeus, chairman of the UN special commission in charge of scrapping Iraq's weapons of mass destruction, has completed his work.
But Mr Ekeus dashed hopes of a speedy end to the embargo when he said in a report distributed on Monday that Iraq had failed to account for large quantities of "growth media" that could be used to produce bacteriological weapons.
This week France and Russia have been negotiating intensively on the limited-oil sale resolution. "A deal is within reach," the Russian ambassador, Sergei Lavrov, said.
A 1991 Gulf War ceasefire resolution ties sanctions on exports of goods such as oil to a clean bill of health on weapons.