The ousting of Assad, who along with his late father, former president Hafez al-Assad, had forged a close alliance with Moscow, has thrown the future of Russia's bases - the Hmeimim airbase in Latakia and the Tartous naval facility - into question.
Satellite footage from Friday shows what appeared to be at least two Antonov AN-124s, among the world's largest cargo planes, at the Hmeimim base with their nose cones open, apparently preparing to load up.
At least one cargo plane flew out on Saturday for Libya, a Syrian security official stationed outside the facility said.
Syrian military and security sources in contact with the Russians told Reuters that Moscow was pulling back its forces from the front lines and withdrawing some heavy equipment and senior Syrian officers.
But the sources, who spoke on condition of anonymity due to the sensitivity of the situation, said Russia was not pulling out of its two main bases and currently had no intention of doing so.
Some equipment is being shipped back to Moscow as are very senior officers from Assad's military but the aim at this stage is to regroup and redeploy as dictated by developments on the ground, a senior Syrian army officer in touch with the Russian military told Reuters.
A senior rebel official close to the new interim administration told Reuters the issue of the Russian military presence in Syria and past agreements between the Assad government and Moscow were not under discussion.
"It is a matter for future talks and the Syrian people will have the final say," said the official, adding that Moscow had set up communication channels.
"Our forces are also now in close vicinity of the Russian bases in Latakia," he added without elaborating.
The Kremlin has said Russia is in discussions with the new rulers of Syria over the bases.Â
Russia's defence ministry did not respond to a request for comment on Reuters reporting.
A Russian source who spoke on condition of anonymity said discussions with the new rulers of Syria were ongoing and Russia was not withdrawing from its bases.
Reuters was unable to immediately ascertain how Syrian rebel leader Ahmad al-Sharaa - better known as Abu Mohammed al-Golani - saw the long-term future of the Russian bases.
Russian President Vladimir Putin granted ousted president Bashar al-Assad asylum in Russia. (AP PHOTO)
Russian President Vladimir Putin, whose 2015 intervention in the Syrian civil war helped prop up Assad when the West was calling for him to be toppled, granted Assad asylum in Russia after Moscow helped him to flee on Sunday.
Moscow has backed Syria since early in the Cold War, and had recognised its independence in 1944 as Damascus sought to throw off French colonial rule. The West long regarded Syria as a Soviet satellite.
The bases in Syria are an integral part of Russia's global military presence: the Tartous naval base is Russia's only Mediterranean repair and resupply hub, with Hmeimim a major staging post for military and mercenary activity in Africa.
Russia also has eavesdropping posts in Syria which were run alongside Syrian signals stations, according to Syrian military and Western intelligence sources.
The Tartous facility dates from 1971, and after Russia intervened in the civil war to help Assad, Moscow was in 2017 granted a free of charge 49-year lease.
Yoruk Isik, a geopolitical analyst based in Istanbul who runs the Bosphorus Observer, said that Russia was probably sending cargo planes out of Syrian via the Caucasus, and then on to the Al Khadim air base in Libya.
On the highway linking the Hmeimim air base to the base in Tartous, a Russian convoy of infantry fighting vehicles and logistics vehicles could be seen driving toward the air base, a Reuters journalist said.
At Hmeimim, Reuters saw Russian soldiers walking around the base as normal and jets in the hangars.
Satellite imagery taken on December 9 by Planet Labs showed at least three vessels in Russia's Mediterranean fleet - two guided missile frigates and an oiler - moored around 13km northwest of Tartous.