National Security Agency (NSA) contractor gave an interview to Russian television and said he wanted 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.
Under mounting pressure over the leaks, Washington on Wednesday declassified some details of its phone-tapping scheme.
Three secret documents, including a court order authorising the collection of US phone records, were released "in public interest", according to director of national intelligence James Clapper. The order spells out how the government can use call data obtained from telecom giants such as Verizon.
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.