The whistleblower, who will face felony charges if he returns to the US, has been described by Trump as “a traitor”.
He has been living in exile in Russia since June 2013 – initially for just one year but officials later extended Snowden’s asylum agreement – and claimed they would not be interested in trading the former CIA worker.
But now US intelligence reports have suggested Russian authorities could hand him over to the US to “curry favour” with the new President.
Snowden could be handed over to Trump by Putin
Edward Snowden has lived in exile in Russia since 2013
He tweeted: “Days ago, I criticised the Russian government's oppressive new "Big Brother" law. Now, threatening rumours. But I won't stop.
“I don't know if the rumours are true. But I can tell you this: I am not afraid.
“There are things that must be said no matter the consequence. Don't be afraid. Be ready. There are more of us than them.”
Snowden insisted he was not afraid of extradition
He also urged supports not to be afraid
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Russia's immigration service extended Snowden's residency permit to 2020
I don't know if the rumours are true. But I can tell you this: I am not afraid.
Whistleblower Edward Snowden
The former National Security Agency (NSA) contractor shook the American intelligence establishment after a series of devastating leaks on mass surveillance in the US and around the world.
In January, Russia's immigration service extended Snowden's residency permit to 2020.
But according to a US intelligence report, Russia has now toyed with the idea of handing over Snowden as one of a string of initiatives to appease Donald Trump.
Vladimir Putin in pictures Tue, December 13, 2016
Russin President Vladimir Putin in pictures
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It comes as Putin and Trump embrace hopes of a stronger union between the two Cold War nations, and look to negotiate sanctions imposed by the Obama administration on Russia.
While Snowden’s lawyer has claimed he has received “no such signals” of a deal, the whistleblower has said he is “encouraged” by the news.
Vladimir Putin could be about to "gift" Snowden to Trump
He said: “It wasn’t that many years ago that people were saying ‘this guy is a Russian spy’ –but countries don’t give up their spies.
“And if my recent criticisms of Russian internet policies, criticism of their human rights have been so severe that even my greatest critics in the intelligence community are now saying ‘he’s a liability, they want to get him out of there’, that’s a vindication of the fact I’m independent.”
Russian foreign ministry spokeswoman Maria Zakharova responded by condemning what she called a proposal to "hand over those who seek protection."
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