US whistleblower Edward Snowden "has most likely already left Russia", according to the Russian news agency Interfax.
"He could have left by a different plane," a source was quoted as saying, pointing out that Snowden might be on an aircraft other than the Moscow-Havana flight of 10:05GMT that he was widely expected to take earlier on Monday.
Ecuador earlier said it had received a request for political asylum from Snowden, the fugitive US intelligence contractor, adding that the application was still being "analysed" with no decisions taken yet.
He was expected to fly to Ecuador via Cuba provided he got a positive reply to his asylum request.
Meanwhile, the White House asked the Russian government to "look at all options available" to send Snowden back to the US to face espionage charges. The call has not received a positive reponse.
The US secretary of state, John Kerry, said that ties with Russia and China could be affected, saying it would be "disappointed" if Snowden was allowed to board a plane. He said the US expected "reciprocity" from Russia because it had transported seven prisoners that Moscow wanted in the past two years.
"I wonder if Mr Snowden chose China and Russia as assistants in his flight from justice because they are such powerful bastions of internet freedom," Kerry said while on a trip to New Delhi.
Snowden, who has revealed secret documents on US internet and phone surveillance activities, flew from Hong Kong to Moscow on Sunday and was reported to have met the Ecuadorean ambassador in the Russian capital after applying for asylum.
Regarding Snowden's asylum request, Ecuador's foreign minister Ricardo Patino said: "We will make a decision... we are analysing it."
"It [the request] has to do with freedom of expression and the security of citizens around the world. We always act by principle not in our own interest. There are some governments who act more on their own interests, we do not," he added during an official visit to Vietnam.
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Earlier, Patino wrote on Twitter that Snowden had applied for asylum.
Meanwhile, anti-secrecy website WikiLeaks said in a sytatement, "Mr Snowden ... is bound for the Republic of Ecuador via a safe route for the purposes of asylum, and is being escorted by diplomats and legal advisers from WikiLeaks."
WikiLeaks founder Julian Assange is currently sheltered by Ecuador's embassy in London as he fights extradition to Sweden on sex assault charges, which might also lead him to be sent to the US, where he faces charges similar to Snowden's.
Al Jazeera's Peter Sharp said that Snowden did not have a legal passport as it was revoked by the US, adding that he had been using Ecuadorian documents to travel.
“He is looking for a country who can offer him a long-term asylum, because this is not going to end overnight,” Sharp said.
Snowden's application came days after Washington charged him with spying and espionage following his leak to western newspapers of the Prism spying programme run by his former employer, the National Security Agency.
In a statement, Washington criticised Hong Kong and China for allowing Snowden to flee.
A statement by Hong Kong authorities earlier on Sunday said it had "not obtained adequate information" to handle a provisional arrest warrant for Snowden issued by the US.
Hong Kong, a former British colony, reverted to Chinese rule in 1997 but retains an independent legal system and its own extradition laws.
Leaks by Snowden revealed that the US had hacked Hong Kong and Chinese institutions.
Snowden also provided documents to the Guardian newspaper that showed British spies were obtaining the contents of 600 million private communications a day by tapping the world's network of fibre-optic cables. They also passed the information to their US counterparts.
The intercepts include emails, telephone calls, Google searches and Facebook updates.