"He is thinking about it. He has a desire to return and we are doing everything we can to make it happen," Anatoly Kucherena, the Russian lawyer who represents the former National Security Agency contractor, told a news conference.
Snowden was given political asylum in Russia in the summer of 2013 after the US revoked his passport. He now leads a reclusive life there.
"With a group of lawyers from other countries, we are working on the question of his return to America," Kucherena said.
The lawyer said Snowden had so far only received a guarantee from the US Attorney General that he will not face the death penalty.
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He said that Snowden is able to travel outside Russia since he has a three-year Russian residency permit, but "I suspect that as soon as he leaves Russia, he will be taken to the US embassy."
Kucherena's comments came at a presser where he presented a thriller loosely based on his encounters with Snowden.