Bush has decided to name a special envoy to try to end violence in Sudan's bloodied Darfur region.
A US official says president Bush's choice may be announced in his speech to the United Nations General Assembly later today.
Another US official said the former head of the US Agency for International Development, Andrew Natsios, was "a good place to put your money."
On Friday, Mr Bush said that he was "frustrated" by UN inaction in the face of what he has repeatedly called "genocide" in the Sudanese province, suggesting that UN peacekeepers be deployed there whether Khartoum likes it or not.
AU extension 'favoured'
Meanwhile Sudan has signalled it will likely extend the mandate of African Union peacekeepers in the war-torn Darfur region after their mandate expires on September 30.
As the African Union’s (AU) 15-member Peace and Security Council (PSC) prepared to meet in New York, Sudanese Vice President Ali Osman Taha said the mandate of the cash-strapped, 7,000-strong force should be extended
The PSC meeting was scheduled for Monday, but was postponed two days because presidents Olusegun Obasanjo of Nigeria and Paul Kagame of Rwanda could not attend on time.
Britain's Guardian newspaper quoted presidential adviser Ghazi Salahuddin Atabani as saying Sudan may allow AU troops to remain in Darfur past the deadline with more help from the West.
"It is likely we will arrive at an extension of the African Union mandate when the ministers meet in New York. There seems to be a common interest. It will give time for all sides to find a way out of this," Mr Atabani said.
Mr Atabani said Sudan wanted to explore what it called "African Union Plus", whereby AU peacekeepers remain in Darfur but get help in the form of helicopters and surveillance technology from Western states.
The conflict in Darfur between rebels and government-backed Arab militia began in February 2003 and has left more than 300,000 people dead and 2.5 million displaced, creating one of the world's worst humanitarian crises.
The under-funded and badly equipped AU troops have failed to stop the violence.
Sudan rejects UN troops
Late last month, the UN Security Council adopted a resolution calling for the deployment of up to 20,000 UN peacekeepers to replace the AU contingent in Darfur.
But President Bashir, as recently as Saturday, said that under no circumstances would he allow the UN troops into Darfur. He has likened a UN presence to an invasion force bent on regime change in Khartoum.
Last May, Khartoum signed a peace accord in Nigeria with the main Darfur rebel group. But two other insurgents have refused to sign it.
Darfur’s main rebel faction said UN peacekeepers were needed to protect civilians in the war-torn region.
"We welcome the (Security Council) resolution and support it as a guarantee to the protection of our civilian people in Darfur," said Mahjub Hussein, a spokesman for the faction of the Sudan Liberation Movement (SLM) led by Minni Minnawi.
Meanwhile UN chief Kofi Annan was to attend Wednesday's PSC gathering to formally ask the AU to keep its troops in Darfur until the end of the year ahead of the eventual deployment of a UN force.
US Secretary of State Condoleezza Rice discussed Darfur with her Chinese counterpart Li Zhaoxing in New York on Monday.
State Department spokesman Sean McCormack said Ms Rice had "urged the Chinese to do everything they could do to allow in the international force, to allow for that transition from the AU mission to the UN force."
China, a veto-wielding permanent member of the Security Council, has close energy ties with Sudan.
Mr Li said he planned to meet Sudanese President Omar al-Beshir in New York and "would work to persuade the Sudanese to abide by the Security Council resolution”.