A federal law enforcement source told CNN on Monday that the government's investigation will include searches of Snowden's home and efforts to interview his girlfriend, relatives, co-workers and friends.
The official did not know if the FBI would attempt to contact Snowden overseas and ask if he would agree to a voluntary interview, or if the agency would wait until other evidence had been gathered.
While Snowden said he fled to Hong Kong in hopes of avoiding extradition, what's next for him remains unclear.
Although Hong Kong is part of communist-ruled China, the former British colony has a separate system of government that allows a free press and tolerates political dissent.
But legal experts say Hong Kong's extradition treaty with the United States could make it hard for Snowden to successfully fight any proceedings against him unless he is able to prove, for example, that any charges against him are politically motivated.
Patricia Ho, a lawyer with Daly & Associates in Hong Kong, whose firm has handled asylum and refugee claims, said that given Hong Kong's lackluster track record on granting asylum, she was surprised that Snowden had lauded the territory for its commitment to civil liberties.
"Within China itself, Hong Kong has better civil liberties, but I couldn't see the Hong Kong government granting him asylum given their present practices," she said.
On Monday, the office of Russian President Vladimir Putin's spokesman tweeted that U.S. officials had broken the law with the surveillance programs, making Snowden a "human rights activist."
Spokesman Dmitry Peskov told CNN that Russia would consider an asylum request from Snowden but has not received one.
Google on Tuesday asked for permission to publish details of requests for information under the Foreign Intelligence Security Act. It wants to regain the trust of users after initial assertions that it and other companies were providing the NSA with direct, unrestricted access to data stored on their computers.
"Assertions in the press that our compliance with these requests gives the U.S. government unfettered access to our users' data are simply untrue," the company said in a letter to Attorney General Eric Holder and FBI Director Robert Mueller.
But government laws demanding secrecy about the requests "fuel that speculation," the company said.
"Google's numbers would clearly show that our compliance with these requests falls far short of the claims being made," the company said. "Google has nothing to hide."
A Justice Department spokeswoman said officials have received Google's request and are reviewing it.