Snowden, who is holed up in the transit area of Moscow's airport, has asked for temporary asylum in Russia and his attorney said Wednesday once some legal papers are formalized, he will be able to leave the zone, possibly in the next few days, CNN reported.
In Washington, U.S. Sen. Lindsey Graham, R-S.C., said he thought the United States should boycott the 2014 Winter Olympics in Russia if Moscow grants asylum to Snowden.
"I would. I would just send the Russians the most unequivocal signal I could send them," the South Carolina Republican told The Hill when asked about the boycott possibility.
"At the end of the day, if they grant this guy asylum, it's a breach of the rule of law as we know it and is a slap in the face to the United States," Graham said.
Graham's comments to The Hill made him the first senator to propose linking Russia's handling of Snowden, who leaked National Security Agency secrets, to U.S. participation in the Winter Olympics in Sochi Feb. 7-23.
At the White House, press secretary Jay Carney was asked by a reporter if a boycott was "a bad idea."
"Yes," Carney replied. "But it's not one that is an issue right now because we're engaged with the Russians and other governments in helping bring about a positive resolution to this matter.
Also Wednesday, U.S. House Speaker John Boehner, R-Ohio, rejected any suggestion of a U.S. boycott the 2014 Winter Olympics in Russia if that country gives Snowden asylum.
Boehner said fellow Republican Graham is "dead wrong" for proposing the United States boycott because of the fugitive.
Speaking at a news conference in Washington Wednesday, Boehner said: "Listen, I love Senator Graham. We've been close friends for 20 years. But I think he's dead wrong. Why would we want to punish U.S. athletes who have been training for three years to compete in the Olympics over a traitor who can't find a place to call home?"
The U.S. Olympic Committee said Wednesday a U.S. boycott of the Winter Games in Russia would only hurt American athletes, The Hill reported.
"If there are any lessons to be learned from the American boycott of 1980, it is that Olympic boycotts do not work," U.S. Olympic Committee spokesperson Patrick Sandusky said in a statement. "Our boycott of the 1980 Olympic Games [in Russia] did not contribute to a successful resolution of the underlying conflict [the Soviet invasion of Afghanistan]. It did, however, deprive hundreds of American athletes, all whom had completely dedicated themselves to representing our nation at the Olympic Games, of the opportunity of a lifetime."
Other lawmakers have urged President Barack Obama to respond sternly if Russia offers asylum to Snowden, but they haven't mentioned the Olympics.
"There's many things we can do, but I think the experience of canceling the Olympics the last time around wasn't very good," Graham ally Sen. John McCain, R-Ariz., told The Hill. The United States boycotted the 1980 Summer Olympics in Moscow to protest the Soviet invasion of Afghanistan. Four years later, Russia boycotted the Summer Olympics in Los Angeles.
Snowden should receive a certificate within a few days showing his asylum request is under consideration and allowing him to legally leave the airport's transit area, attorney Kucherena said.
"Therefore I think this issue will be resolved within a week and after this the question of granting him temporary asylum will be decided upon," the lawyer said.
Snowden has been in the transit zone of Moscow's Sheremetyevo International Airport since arriving from Hong Kong June 23.
Snowden is charged with espionage for leaking details about the NSA's electronic surveillance programs that logs U.S. phone calls and intercepts international Internet communications with help from U.S. companies.
Snowden sought temporary asylum in Russia instead of political asylum, which requires only an administrative decision by the Russian Federal Migration Service rather than President Vladimir Putin's approval, a spokesman for Russian President Vladimir Putin said.
Putin told reporters in Moscow Wednesday ties between the United States and Russia "are far more important than an intelligence scandal."
He said he believes Snowden "never intended to stay here, in Russia, forever."
Putin has said asylum for Snowden was possible if he stops harming U.S. interests.
"We warned Mr. Snowden that any of his activities that cause damage to U.S.-Russian relations are unacceptable to us," Putin said Wednesday.