Anatoly Kucherena told The Associated Press that Snowden applied to Russia's migration authorities "a long time ago" since his one-year permit is expiring at the end of July.
Kucherena refused to say what kind of migration status his client is seeking, saying that it is up to the Federal Migration Service to make the decision.
Snowden was stranded in a Moscow airport last year on his way from Hong Kong to Cuba, shortly after he revealed the NSA's sprawling program of tapping phones. He received asylum in Russia, attracting the ire of the United States.
The American who leaked a trove of material from the super-secret National Security Agency has kept a low profile in Russia, has never been seen in public or talked to local journalists. His whereabouts are unknown.
Kucherena insisted that the secrecy is necessary for Snowden's protection while skeptics argued that Snowden was living under the surveillance of the Russian secret services.
A Kremlin-connected website has published several pictures of Snowden indicating that he either lives in Moscow or visits it often.
Snowden appeared on President Vladimir Putin's call-in show in April when he asked a question about surveillance in a pre-recorded video message.