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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At least 100 people are feared dead in the bombing including soldiers and Nigerians working for Doctors Without Borders.
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Ms Saward was the first person to waive her right to anonymity when she was raped at the age of 21 and became a sexual violence campaigner.