An unnamed Russian source close to the matter told the Interfax news agency that Moscow had so far received no formal extradition request from the United States.
"There have been contacts at an unofficial level, along diplomatic channels, with a request to detain and deport" Snowden, the unnamed official said.
But considering current strains in Russian-US relations over human rights issues and the Syria conflict, Moscow has refused to respond, the source said.
"The situation around Snowden is at a dead end."
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Snowden spent Thursday holed up in a Moscow airport transit zone for a fifth day, awaiting a decision on his request for political asylum in Ecuador.
The 30-year-old arrived in Moscow from Hong Kong on a regular Aeroflot airlines flight on Sunday.
The Russian source suggested that the situation will only be resolved once Ecuador or some other country decides to grant Snowden political asylum.