Assad last spoke on June 3 when he addressed parliament in Damascus.
In past speeches he has always referred to the rebels as "terrorists" financed from abroad.
The pro-Syrian Lebanese daily, Al-Akhbar, said Assad was ready to offer a "solution" to the conflict.
Citing anonymous sources, the paper said Assad may submit a five-point plan that would not preclude him from contesting the next presidential election when his current term ends in 2014.
The plan also provides a ceasefire, allowing international observers to monitor its application, a constituent assembly to draft a new constitution, forming a national government and holding free elections for a new parliament, it said.
During his latest visit to Damascus, UN-Arab League peace envoy Lakhdar Brahimi had mentioned a plan, based on the Geneva declaration, that talked of a ceasefire, forming a government and holding parliamentary and presidential polls.
The Geneva plan put forward last June would see a transitional government in place, but it does not refer to Assad going -- a condition the opposition insists on.
The Syrian authorities have not responded directly to Brahimi's plan, which the envoy believes could be adopted by the international community, but have said that they are ready to respond to any plan through dialogue.
But the bloodshed rages on unabated with at least 57 people, among them 25 civilians, killed on Saturday, according to the Syrian Observatory for Human Rights.
NATO-member Turkey, a one-time Damascus ally, has become one of its most vocal opponents over the conflict in its southern neighbour, and on Saturday the deployment began of US Patriot missiles near its border with Syria.
"The deployment started early this morning into Incirlik" Air Base in southeastern Turkey, Peter Woodmansee, missile defence chief of the US European Command, told AFP.
"Several aircraft landed very early this morning with the advance party personnel from 3-2 Air Defense Artillery (ADA) -- the Patriot unit -- arriving as well."
The US will transport some 400 troops to Turkey in the coming days to operate two Patriot batteries, the Germany-based US European Command said on Friday.
They will be based at Gaziantep, 50 kilometres (31 miles) north of the border.
Germany, The Netherlands and the United States agreed to supply the ground-to-air missile batteries which Turkey requested after repeated cross-border shelling from Syria, including an October attack that killed five civilians.
The Patriot systems are expected to become operational later this month.
Syria's allies Iran and Russia oppose the Patriot deployment, fearing that it could spark a regional conflict that also draws in NATO.
"This mission is purely defensive in nature," Woodmansee said.
Arab heavyweights Saudi Arabia and Egypt called on Saturday for a "peaceful" solution to the crisis. Both Riyadh and Cairo have urged Assad to quit.
Foreign Minister Ali Akbar Salehi of Iran, a key Assad ally, is due in Cairo on January 9 for talks on the crisis, media reports in Tehran said on Saturday.
On the ground, a shell hit Bab Tuma, a Christian area of Damascus, and a car bomb exploded in the Rokn Eddin district of the city, the Observatory said.
Assad's forces bombarded rebel positions in Aleppo province and clashes broke out in areas around Aleppo international airport, said the Observatory, which gathers its information from medics and activists on the ground.