The offensive would initially target southern and western parts of the insurgent territory, but not yet Idlib city, said the source, an official in the regional alliance backing Assad.
"The final touches for the first stage will be completed in the coming hours," the official added, without saying when it would start.
There were still negotiations over the offensive going on between Russia and Turkey, as well as with Iran which also supports Damascus in the war, the official said.
Assad has turned towards Idlib, where jihadist factions dominate, after Russian-backed victories in recent years that drove the rebels from a mosaic of other areas in Syria.
The insurgents now hold only the territory in and around Idlib, as well as an adjacent rebel area in which opposition authorities are backed by Turkish armour and money, and a patch of desert around a US military camp in the south.
A major offensive, where displaced people already make up half the population, risks forcing another 700,000 Syrians from their homes, the United Nations says.
UN Secretary-General Antonio Guterres warned Wednesday that full-scale military operations in Syria's Idlib province could lead to a "humanitarian catastrophe" and cautioned against the use of chemical weapons.
"The Secretary-General is deeply concerned about the growing risks of a humanitarian catastrophe in the event of a full-scale military operation in Idlib province in Syria," a UN statement said.
"The Secretary-General once again reaffirms that any use of chemical weapons is totally unacceptable."
He appealed urgently to the Syrian government and all other parties "to exercise restraint and to prioritize the protection of civilians."
Tensions with Turkey
It also risks raising tensions with Turkey, whose army established a ring of observation posts around the rebel territory last year under a "de-escalation" deal with Russia and Iran.
Turkish Foreign Minister Mevlut Cavusoglu said this month he hoped Ankara and Moscow could find a solution for Idlib, warning that a bombing campaign there would be a massacre. Ankara also fears a major offensive could unleash a new flood of refugees across the Turkish border.
Lavrov said on Wednesday there was a political understanding between Russia and Turkey on the need to distinguish between the Syrian opposition and people he described as terrorists in Idlib.
According to western estimates, some three million people are at risk in the province, which borders Turkey.
An offensive by the Syrian government, which wants to retake the province with the backing of Moscow, would have explosive repercussions for civilians as well as for moderate rebels and radical Islamists.
Chemical weapons attack?
During closed-door talks at the UN Tuesday that were requested by Russia, Moscow claimed, without evidence, that "white helmet" rescue workers were preparing a chemical attack in Idlib, according to diplomats, who called the allegations "very bizarre."
Western powers view those claims as an attempt to deflect attention from preparations for a Syrian military offensive.
According to the diplomats, western powers have given the UN Security Council the names of Syrian commanders and regiments involved in the preparations for an offensive in Idlib, who could be held responsible in the event of attacks on civilians.
During a public session on Syria at the UN Tuesday, Russia denied any possibility of a chemical attack in Idlib by the Syrian government.
Russia's Ambassador Vassily Nevenzia insisted that the Syrian military has no chemical weapons and did not intend to use any.