Revealing the details of the plan for the first time, Russia's Kommersant daily said it had been given to the American side on Tuesday, although Russia only announced on Wednesday evening that the plan had been passed on.
As a first step, Damascus would join the Organization for the Prohibition of Chemical Weapons (OPCW), Kommersant said, quoting a Russian diplomatic source.
Then Syria would have to declare the location of the chemical weapons arsenals and where they are made. The third step would be allowing OPCW inspectors into Syria to examine them.
The final step would be deciding, in cooperation with the inspectors, how to destroy the weapons.
Kommersant, which is known for its strong foreign ministry sources, said that who would physically destroy the weapons has yet to be decided but it was not excluded that the United States and Russia could do this jointly.
Russian Foreign Minister Sergei Lavrov and US counterpart John Kerry are due to discuss the plan in Geneva in talks Thursday.
Kommersant said that it was the American side who requested the talks after receiving a copy of the details of the Russian plan.