The former U.N. chief Annan, in his capacity as U.N.-Arab League envoy, will visit Assad on Saturday and also plans to meet the Syrian opposition before leaving the country on Sunday.
Annan has called for a political solution, but dissidents say there is no room for dialogue amid Assad's crackdown.
"If (Annan) can persuade Russia to back a transitional plan, the regime would be confronted with the choice of either agreeing to negotiate in good faith or facing near-total isolation through loss of a key ally," the Brussels-based International Crisis Group said in a paper this week.
China and Russia have opposed any U.N. resolution, fearing Libya-style military intervention. Germany's Foreign minister Westerwelle said he hoped that Russia will change its mind after Vladimir Putin has won the presidential elections. France's Foreign Ministry said Paris would not accept any U.N. Security Council resolution which would assign responsibility for the violence in Syria equally between the Syrian government and the opposition. But Foreign Minister Alain Juppé denied Russian suggestions the that West was seeking a pretext for military action against Assad: "The option of any military intervention is not on the table," he said.
China, which despatched an envoy to Syria this week, said on Friday it would send an assistant foreign minister to the Middle East and to France to discuss a way forward. Beijing urged Annan to "push for all sides in Syria to end their violence and start the process of peace talks".
U.N. humanitarian chief Valerie Amos, who visited Homs this week, said Assad's government had agreed to join U.N. agencies in a "limited assessment" of civilian needs in Syria, but had not met her request for unhindered access for aid groups. Amos said she was "devastated" at the destruction she saw in Homs. The United Nations estimates at least 25,000 refugees have fled Syria in the past year. The U.N. figures were based mainly on refugees who have registered with the UNHCR. Many have fled to neighbouring countries without registering. Significant numbers of Syrians are also thought to be displaced within the country. Syrian security forces have killed well over 7,500 people since the anti-Assad uprising began a year ago, according to a U.N. estimate. The government said in December that "armed terrorists" had killed more than 2,000 soldiers and police.