If the talks are successful, this would be the first time rebels will have been evacuated from Syria's capital since the country's conflict broke out six years ago.
Several evacuations of insurgents and their families have already taken place in towns and cities in Damascus province.
"Negotiations are taking place between intermediaries in the Barzeh and Qabun districts and the authorities on evacuating rebels and their families," the source said, speaking on condition of anonymity.
Evacuations from Barzeh could begin as early as Monday, the source added, without elaborating on numbers.
The negotiations follow Saturday's start of a "de-escalation" process put in place by regime allies Russia and Iran and rebel-backer Turkey in four regions of Syria.
Damascus is excluded from the multi-phase safe zones plan.
Rebels and their jihadist allies currently operate in five districts of the capital.
In the northeast, they control most of Qabun and Tishrin, and in the east they control about half of Jubar.
Rebels are also present in the north of the city in the Barzeh neighbourhood and in the south in Tadamun.
Qabun has seen fierce fighting for weeks as President Bashar al-Assad's forces advance on rebels.
According to the Syrian military source, a "ceasefire until midnight was concluded with a view to reaching a compromise concerning the two districts" of Barzeh and Qabun.
Britain-based monitor the Syrian Observatory for Human Rights also reported the negotiations.
"Barzeh and Qabun are calm because talks are under way on what would be the first evacuation of its kind in the capital," Observatory chief Rami Abdel Rahman told AFP in Beirut.
He said an evacuation would affect several thousand rebels and civilians, and that its timing was still under discussion.
At the end of April, a vast operation took place in which nearly 11,000 people were evacuated from besieged rebel-held and loyalist areas.
The rebels, who have lost large areas to government forces, have been forced to sign deals to evacuate many of their strongholds.
Syria's conflict erupted in March 2011 with the repression of pro-democracy protests.
Since then, more than 320,000 people have been killed and millions displaced, and the war has become more complex as regional and international powers have been drawn in.