Anatoly Kucherena said the question "has not been solved yet," ITAR-Tass reported.
He said Snowden took the news "with understanding."
Russian media reported earlier in the day the Federal Migration Service had given the former contractor for the U.S. National Security Agency papers that would allow him to leave the Sheremetyevo International Airport, where he has been holed up in the airport's transit zone since he arrived in Moscow June 23.
The attorney said the documents Snowden received earlier from the migration service do not allow him to leave the airport, RT reported.
"The certificate is not a document," Kucherena said. "Political asylum request may be received within three months."
Kucherena said Snowden has good accommodations at the airport.
Snowden, who applied for temporary asylum in Russia last week, is wanted in the United States for leaking information about the National Security Agency's massive surveillance programs. He faces espionage charges and the United States has warned countries that have said they would consider granting Snowden asylum not to accept him.
A source told Interfax Snowden and Kucherena talked in the transit zone.
Wednesday is the deadline for the review of documents Snowden submitted last week to Russia's Federal Migration Service.
Kucherena had said Snowden could decide to become a permanent resident in Russia rather than trying to seek asylum elsewhere.
"He's planning to arrange his life here," Kucherena told state-funded Russian TV network RT. "He plans to get a job. And, I think, that all his further decisions will be made considering the situation he found himself in."
The Obama administration has been pressing Russia to detain Snowden and return him to Washington.