Lonnie Snowden said Friday he made the offer in a letter by a lawyer, Bruce Fein, to the Justice Department, the Los Angeles Times reported.
The condition include that his son, Edward Snowden, remain free before trial, not be subjected to a gag order and be given the choice of where his trial would be held.
"We believe you share our objective of securing Edward's voluntary return to the United States to face trial," Fein said in his letter to U.S. Attorney General Eric H. Holder Jr.
Edward Snowden, 30, is currently in a transit area at the Moscow airport. Russian President Vladimir Putin has refused to extradite him but has also refused to admit him to Russia.
Lonnie Snowden said on NBC's "Today" he has not seen his son since April.
"I love him. I would like to have the opportunity to communicate with him. I don't want to put him in peril, but I am concerned about those who surround him," Lonnie Snowden said. "I don't believe he has betrayed the people of the United States."
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