Snowden applied for temporary asylum in Russia last week after his attempts to leave the airport and fly out of Russia were thwarted. The United States wants him sent home to face prosecution for espionage.
Snowden, who revealed details of NSA's wide-ranging spying activities targeting data and phone communication, is believed to have been staying at the transit zone of Moscow's Sheremetyevo airport since June 23, when he arrived on a flight from Hong Kong.
RIA Novosti quoted an unnamed security official on Wednesday as saying that Snowden has been issued documents, allowing him to formally enter Russia.
President Vladimir Putin has said that Snowden can be granted asylum in Russia only if he stops leaking secrets.
A spokeswoman for the Federal Migration Service told the Associated Press they had no information about the status of Snowden's application for asylum.
Granting Snowden asylum would add new tensions to U.S.-Russian relations already strained by criticism of Russia's pressure on opposition groups, Moscow's suspicion of U.S. missile-defense plans and Russia's resistance to sanctions against the regime of Syrian President Bashar Assad.