Fein is working with Kucherena and "expects to coordinate a visit to Moscow with Mr. Snowden within the next six weeks," Fein told CNN.
On Wednesday night, Fein appeared on "Anderson Cooper 360" and said that Snowden was in good health in Russia and that his lawyer was open to hammering out an ending that would satisfy all.
Fein relayed the conversation he had with Kucherena, he told Cooper.
"There may be a time where it would be constructive to try and meet and see whether there can't be common ground that everyone agrees would advance the interest, the United States, Mr. Snowden, Lon, his father, and the interest of Russia in trying to resolve this in a way that honors due process and the highest principles of fairness and civilization," Fein said.
Kucherena earlier told Russian news agency Itar-Tass that he'd start working on Lon Snowden's visa application.
"I telephoned him (Edward Snowden) today. We agreed that I would prepare an invitation for his father to visit Russia. I hope that the visa formalities will not be long," Kucherena said Wednesday.
Fein has objected to the government's intent to prosecute Snowden.
"The majority of the American people now have voiced grave concerns about the scope of that program. And it seems somewhat odd to be prosecuting somebody for disclosing government wrongdoing."
He said that Snowden had the courage to spark a conversation that Obama has called "urgent."
Snowden leaks again
On Wednesday, Snowden once again made himself a thorn in the side of the NSA.
The British daily The Guardian, which broke news of the NSA programs on the surveillance of phone and Internet metadata after Snowden leaked the information, revealed yet another NSA data collecting scheme.
The report says that according to the leaked documents, XKeyscore allows intelligence agents to see anything you've ever done on the Internet. With ease, they can observe your browsing history, searches, e-mails, chats and more, the report says, and it does not require a search warrant.
After the article was published, Snowden came forward as the source.
FBI and Snowden's father
Snowden's father told Anderson Cooper that the FBI had wanted to fly him to Moscow to encourage the National Security Agency leaker to come home to the United States.
But Lon Snowden said he backed out because it was not clear he would be able to speak to his son.
When he asked FBI agents if they would be able to set up communications, they hesitated, he said. And that made him suspicious.
"I'm not going to get on a flight and go to Moscow and sit on a tarmac to be an emotional tool for you to use against him. I want to first be able to speak to my son," he said he told the agents.
Lon Snowden has previously said that he wants his son to stay in Russia until he is confident he can get a fair trial in the United States.
"I am not confident at all," he said.
Even though Manning was found this week to be not guilty of aiding the enemy -- one of most serious charges he faced -- the fact that the soldier was convicted of 20 charges including several under the Espionage Act made Snowden's father uneasy, he said.
But, he added, his son's case is "completely different" from Manning's.
"I think my son has exercised discretion in the information that he has shared," he said.
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