Mr. Annan discussed the so-called "hybrid force" proposal in a telephone conversation Tuesday with Sudanese President Omar al-Bashir.
The call came a day after the Sudanese leader told a video news conference his government would not accept UN-backed foreign troops in Darfur.
Two weeks ago, after a high-level meeting on Darfur in Addis Ababa, Mr. Annan announced that Sudan had agreed "in principle" to a joint African Union-UN mission for the region.
UN officials said the agreement called for a blue-helmeted force of 17,000 troops and 3,000 police officers to bolster an existing 7,000 strong A.U. force.
Since then, however, Sudanese authorities have made conflicting statements about their understanding of the deal.
President Bashir added to the confusion Monday when he said foreign peacekeepers coming to Sudan under a UN Security Council resolution would be considered "colonizing forces."
At the same time, however, he said refusing to accept blue-helmeted troops does not mean Khartoum is not cooperating with the world body.
Secretary-General Annan told reporters Tuesday Mr. Bashir had promised a fuller explanation regarding three questions Sudan had raised about the Addis Ababa agreement.
"The first question was the size of the force, what strength the force should be. The second question dealt with the appointment of the Special Representative, or the High Representative, who would report to both the African Union and the UN, and the appointment of the commander, where they felt that the commander should be an African. And we have no problem with that."
Mr. Annan said the Sudanese reply would be discussed at an African Union summit Wednesday in the Nigerian capital, Abuja. He told reporters he expects African Union leaders to "press ahead" with the agreement reached earlier this month in Addis Ababa.
The secretary-general said he still hopes for progress on Darfur during his remaining time in office. He is due to hand over the UN's top job to Ban Ki-Moon of South Korea at the end of December.