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
The UK has failed to make the top 10 in the best places to be a mother rankings from a leading charity
More than 4,400 community police officers have lost their jobs since 2010, according to Unison
Western and central regions will be prone to thundery, blustery downpours all day