National Security Agency (NSA) contractor gave an interview to Russian television and said he wanted to see his son to be safe.
"Today we agreed over the telephone (together with Edward Snowden) that I will put together an invitation for his father to come to Russia," lawyer Anatoly Kucherena told Russian news agencies.
"I hope that it won't take too long to issue a visa," he said.
Edward Snowden has been staying in the transit zone of the Sheremetyevo airport outside Moscow since he flew in from Hong Kong on June 23 and has never formally crossed the Russian border.
Snowden, 30, is wanted on felony charges by the United States after leaking details of vast US surveillance programmes but Russia has refused to extradite him.
Snowden's father could be issued with a visa invitation by a private individual or a hotel which would then be processed by a Russian embassy.
In his interview to Russian television channel Rossiya 24, Lon Snowden revealed that the FBI had contacted him with an offer to go to Russia, which he had not taken up for fear that he could be used to pressure his son.
He said he did not refuse the offer outright, however, and was considering the possibility of travelling to Russia and even attending the 2014 Winter Olympics in Sochi.
Speaking from a Washington studio, he greeted his son, after the presenter said he had been alerted to watch the show, and told him to stay safe.
"Edward, I hope you are watching this. Your family is well. We love you. We hope you are healthy, we hope you are well, I hope to see you soon, but most of all I want you to be safe. I want you to find a safe haven," Lon Snowden said.
Lon Snowden said in the interview that he hoped his son would return home one day.
But he said that events over the past few weeks suggested that there were no guarantees of a fair trial in the United States, and that he therefore agreed with his son's decision to remain in Russia.
"If it were me, I would stay in Russia. And that's what I hope that my son will do."
"The fact is no assurances have been provided that he would be given a fair trial," he said, speaking after US soldier Bradley Manning was convicted of espionage on Tuesday for leaking US secrets to WikiLeaks.
Britain's Guardian newspaper on Wednesday published further details of documents handed over by Edward Snowden on secret monitoring of emails by the NSA.
Kucherena told the Interfax news agency that Snowden handed the documents over before he arrived in Moscow and had not given anything new to journalists since then.
The head of the Russia's Federal Migration Service, Konstantin Romodanovsky, told the ITAR-TASS news agency that his agency has not processed the initial stage of Snowden's application for temporary refugee status, saying this could take up to three months.
A survey by the Levada independent pollsters released on Wednesday found that 51% of Russians backed Snowden's release of information on the US secret services, and 43% thought he should get asylum in Russia.