The US- and British-sponsored resolution would authorise the deployment of 20,000 UN troops and police in Darfur to take over from 7,000 African Union troops in the western Sudanese region.
Although the resolution, likely to be put to a vote on Thursday, would state that Sudan must agree to the deployment, it was expected to add pressure on Khartoum to drop its opposition.
John Bolton, the US ambassador to the UN, told reporters at the United Nations: "Our judgment here is that we think we've found a formulation that would win acceptance on the [Security] Council."
Omar al-Bashir, the Sudanese president, reiterated on Tuesday his opposition to the deployment.
"We are not advocates of confrontation with the world, but we shall never accept the transition of the AU mandate to any organisation, and we shall never agree to the AU troops changing their hats from [AU] green to [UN] blue," he said.
"...we shall never accept the transition of the AU mandate to any organisation, and we shall never agree to the AU troops changing their hats from [AU] green to [UN] blue"
Sudan has likened the deployment of UN troops to a Western invasion that it says would attract militants and cause an Iraq-style quagmire.
Al-Bashir rebuffed a plea from Washington's top Africa envoy on Tuesday to allow a UN force into Darfur after making her extend her visit to secure a meeting.
Jendayi Frazer, the US assistant secretary of state for African affairs, met al-Bashir on Tuesday and extended him an invitation from the US president to meet him on the sidelines of the UN General Assembly in New York next month.
The US said al-Bashir would send an envoy to Washington soon.