"We are always followed [by somebody]. I don't know which way I should choose to go back home," Anatoly Kucherena said at a media conference.
The lawyer mentioned one incident when his car was chased by five other cars and he was forced to leave his vehicle.
"To be honest, I don't know who these people were, it's hard to tell. It could have been journalists. I don't want to make accusations. At some point I felt like a person who didn't deserve a situation like this," Kucherena said.
Hollywood director Oliver Stone has bought the rights to the book to be used as one of the sources for his upcoming Snowden biopic.
In 2013, Snowden left the United States after leaking confidential data about secret surveillance programs conducted by the NSA and other intelligence agencies. In August 2013, he was granted asylum and subsequently a three-year residency permit by Russia. The former NSA contractor is wanted in the United States on a number of charges, including espionage and government property theft.