Interfax news agency quoted "an informed source in the Russian capital" as saying that "among other possibilities, (Russia may) detain the American in order to check his passport."
The report could indirectly confirm that Snowden was in fact still staying at Moscow's Sheremetyevo international airport, where he is believed to have arrived from Hong Kong on Sunday.
Foreign Minister Sergei Lavrov told reporters that the US intelligence contractor had never crossed Russia's border. But this did not rule out him staying in the transit zone of the airport.
"Where did this theory come from that Snowden is in Russia? No one saw him on the Hong Kong flight and no one saw him at the airport," tweeted Alexei Pushkov, who heads the lower house of parliament's foreign affairs committee.
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Interfax did not specify why Russian authorities may want to check Snowden's passport, which was revoked by the US authorities before he flew out of Hong Kong.
He travelled from Hong Kong on a special refugee pass issued by Ecuador, the nation in which he will seek asylum, according to the anti-secrecy WikiLeaks website.
Interfax had yesterday reported a source as saying that Snowden had "likely" already left Russia.