The visit comes a day after Annan acknowledged in an interview that the international community's efforts to find a political solution to the escalating violence in Syria have failed.
Annan is the architect of the most prominent international plan to end the 16-month crisis in Syria which activists say has left well over 14,000 people dead.
Annan's six-point plan was to begin with a cease-fire in mid-April between government forces and rebels seeking to topple Assad but the truce never took hold.
A statement issued Sunday by spokesman Ahmad Fawzi did not give details of Annan's schedule in Damascus.
Annan acknowledged in an interview published Saturday that the international community's efforts to find a political solution to the escalating violence in Syria have failed.
"The evidence shows that we have not succeeded," he told the French daily Le Monde.
Annan's proposed truce never took hold, and now the almost 300 U.N. observers sent to monitor the cease-fire are confined to their hotels because of the escalating violence.
U.S. Secretary of State Hillary Rodham Clinton said Sunday that time is running out on Syrian peace hopes and warned that the Syrian state could collapse.
Speaking in Japan, Clinton said Annan's acknowledgement that his peace plan is failing "should be a wake-up call for everyone."
She said last month was the deadliest for the Syrian people in the 16-month revolt, but added that the opposition "is getting more effective in defence of themselves and going on the offensive against the Syrian military."
Syria military manoevres
Meanwhile, Syria's military began large-scale exercises simulating defence against outside "aggression," the state-run news agency said Sunday — an apparent warning to other countries not to intervene in the country's crisis.
The exercise began Saturday with naval forces in a scenario where they repelled an attack from the sea, and will include air and ground forces over the next few days, SANA said. State TV broadcast footage of missiles being fired from launch vehicles and warships.
Some in the Syrian opposition have appealed to the West for foreign forces to step in to stop bloodshed that they say has left more than 14,000 dead since the uprising against President Bashar Assad began in March 2011. So far, the West has shown little appetite to intervene militarily in the conflict.
Syrian Defence Minister Dawood Rajiha attended the manoeuvrs and praised the "exceptional performance" of the naval forces which showed "a high level of combat training and ability to defend Syria's shores against any possible aggression."
"The navy carried out the training successfully, repelling the hypothetical attack and striking at given targets with high precision," the report said.