Interfax news agency quotes Russian migration service head Konstantin Romodanovsky as saying no asylum request had been received as yet.
On Friday, the former CIA contractor appeared at a news conference at Moscow's Sheremetyevo Airport alongside representatives from Russian and other international human rights organizations. Snowden said he hoped to go to Latin America after applying for temporary asylum in Russia. He is thought to be considering Bolivia, Nicaragua or Venezuela as possible final destinations.
Meanwhile, NPR's Michele Kelemen reports that the U.S. State Department expressed disappointment that Russia had given Snowden what it described as a "propaganda platform" to espouse his views.
Snowden is believed to have spent the past couple of weeks stuck in a transit area at a Moscow airport. In the past several weeks, The Guardian newspaper has published a series of exposes of U.S. electronic surveillance efforts using Snowden as its source.
American officials say his revelations have hurt national security, but Snowden's supporters say he has exposed violations of civil liberties.
State Department spokeswoman Jen Psaki said Friday that Washington was not pleased at Snowden's Friday news conference.
"We are disappointed that Russian officials facilitated this meeting today by allowing these activists and representatives into the Moscow airport transit zone," she said.
Psaki repeated Washington's position that it doesn't see Snowden as a whistle-blower, but as someone who faces felony charges in the United States.