By Justin Sink - 07/18/13 12:28 PM EDT
The book could complicate the travel plans of his source, however. Earlier this week, Snowden asked Russian authorities to grant him temporary asylum and allow him to leave the transport zone of Moscow's international airport.
Russian President Vladimir Putin has said that Snowden could only stay in Russia if he stops "harming" the United States through the release of more intelligence information.
A lawyer with ties to the Kremlin told Russia's Interfax news agency that Snowden would "abide by the conditions" imposed by Russian authorities, if necessary.
This will be Greenwald's fifth book.