The charges are said to have been filed by federal prosecutors in the Eastern District of Virginia, whose jurisdiction includes the main base of Mr Snowden's former employer, Booz Allen Hamilton.
The Post report said the US Justice Department had declined to comment on the claims.
More top news
Billionaire Microsoft co-founder Paul Allen has claimed discovery of the Japanese battleship Musashi that was sunk by the US Navy in 1945.
Friday will be mostly dry with sunny spells for much of the UK. Temperatures will be mild across the country.
Some famous Liberal Democrat names will be fighting for their political lives in the election, now just over two months away.