Anatoly Kucherena, who has represented Snowden since his arrival in Russia in 2013, told Interfax news agency that "Russia has no legal basis to hand over Snowden."
US channel NBC yesterday quoted a senior US official with access to highly sensitive intelligence reports as saying Russia was considering the move "to curry favour" with Trump.
Snowden's US lawyer Ben Wizner told NBC that he was not aware of such plans.
"All this talk is just ordinary speculation. Someone is indulging in wishful thinking," Kucherena said, insisting that Snowden "lives in Russia absolutely lawfully."
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He has been living in exile in Russia since the summer of 2013 after spending weeks in the transit zone of Moscow's Sheremetyevo airport.
Russia's immigration service in January extended Snowden's residency permit to 2020.
"Russia doesn't trade in people and human rights, although American secret services constantly try to draw us into various acts of provocation," Kucherena said.
Snowden wrote on Twitter yesterday that the NBC report was "irrefutable evidence that I never cooperated with Russian intel."
The US has charged him with espionage and theft of state secrets after he released thousands of classified documents in 2013.
Former CIA acting director Michael Morell in an opinion piece in January suggested that Russian President Vladimir Putin could hand over Snowden to mark Trump's inauguration that month.
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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