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.
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The US president is seeking an investigation by the Justice Department.
The casualty was taken into the care of paramedics with a suspected leg injury.
The 16-year-old was discovered with stab wounds on Thursday afternoon.