Annan, in Madrid to attend an anti-terrorism conference, said on Wednesday that his envoy Terje Roed-Larsen would be travelling to the region on Thursday to meet Syrian President Bashar al-Asad and Lebanese President Emile Lahud.
A UN Security Council resolution in September called for foreign troops to leave Lebanon but did not specify a date.
US President George Bush has called for Syrian troops to leave Lebanon before parliamentary elections there in May.
"I am highly interested, after my envoy comes back to report to me at the end of the discussions, on how quickly the withdrawal can take place and I hope he will be able to come back with a full timetable," Annan told a news conference.
Roed-Larsen will meet Egyptian President Husni Mubarak in the Egyptian resort of Sharm al-Shaikh on Thursday before visits to Jordan, Lebanon and Syria, a UN spokesman said.
After talks with Jordanian officials, Roed-Larsen will arrive in Beirut on Friday to present his condolences to the family of the late prime minister Rafiq al-Hariri, Negib Friji said.
"He will travel to Damascus on Saturday to meet Syrian leaders and will return Sunday to Beirut to meet with the president, the parliament speaker, the prime minister and the foreign minister," Friji said.
Lebanon's civil war ended in 1990 under Taif Accord, which called for Syrian troops to move to eastern Lebanon for two years, pending a bilateral agreement on full withdrawal.
"The Security Council resolution requires withdrawal to Syria. There has been a suggestion from the Syrian side that they would implement it in compliance with the Taif agreement," Annan said.
"From the Security Council point of view, what is essential is that a full and complete withdrawal takes place regardless of whether it is done under the US resolution, or the Taif agreement or from a decision from the government of Syria."