While Snowden might apply for Russian citizenship, Putin spokesman Dmitry Peskov said the country's diplomatic relationship with the United States was "a priority," RIA Novosti reported Friday.
"Russia has never extradited anyone and never does, but no one, not even Snowden, should be allowed activities that could be detrimental to bilateral Russian-American relations," Peskov said.
Peskov said he didn't know if Snowden had sought citizenship, but the application would be considered if he had.
Snowden submitted a request for temporary asylum in Russia Tuesday.
U.S. President Barack Obama is reported considering canceling a scheduled September trip to Moscow because of the situation with Snowden, who has taken up residence in a section of a Moscow airport where he landed after fleeing Hong Kong in an attempt to escape arrest by U.S. authorities.
Putin's spokesman said he had "neither official information, nor confirmation" of any possible cancellation of Obama's trip.