Snowden, whose exact location is unknown, revealed that he was in the southern Chinese city in an interview with the Guardian newspaper released yesterday, noting his choice of Hong Kong due to its "strong tradition of free speech".
The United States and Hong Kong signed an extradition treaty in 1996, a year before the city was handed over from British to Chinese control, under which both parties agreed to hand over fugitive offenders.
"We don't have anything for you at this point," Deputy for Public Affairs at the US Consulate in Hong Kong Scott Robinson told AFP.
In his interview, Snowden, a 29-year-old government contractor who has been working at the National Security Agency for the past four years, described the consulate as a "CIA station just up the road".
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The Hong Kong Security Bureau, which oversees immigration, the police and intelligence services in the territory, declined to comment.
Snowden also expressed an interest in seeking asylum in Iceland, saying it was a country that stood up for Internet freedoms.
But the Icelandic consulate in Hong Kong said it had "no comment" on the case, refusing to say whether he had been in touch.
Hong Kong is a semi-autonomous territory with its own political and legal system that guarantees civil liberties not seen on the mainland, including freedom of speech and association.
Under the "one country, two systems" principle, the special administrative region has its own constitution, the Basic Law, giving it a high degree of autonomy, although this does not apply to foreign relations and defence.
"Anybody here in Hong Kong should be protected under international standards. We hope anybody here would be dealt with fairly and their rights are respected.