The newspaper said Mr Snowden would be able to challenge the US request for his extradition in court in Hong Kong, where he is understood to be hiding.
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A police spokesman said the incident in the Bourke Street Mall on Friday was not related to terrorism.
The former reality TV star will follow in the footsteps of Abraham Lincoln and John F Kennedy when he takes his oath later on Friday.
The President-elect's comments on Twitter will come under even closer scrutiny when he takes office on Friday.