Attorney General Eric Holder told a Russian official last year that the U.S. would not seek the death penalty for Snowden.

Talk of the idea of clemency for Snowden has come to the fore in recent days. The New York Times editorial board vouched for it last week. So did the Guardian newspaper of Britain.

Snowden has shared information about sweeping surveillance efforts at the National Security Agency with The Washington Post and the Guardian. He was charged with espionage by federal prosecutors last year and has been living in Russia.

Polling shows the American public would be skeptical about offering Snowden leniency. Former Department of Homeland Security secretary Janet Napolitano said she doesn't think the United States should grant Snowden clemency.

"From where I sit today, I would not put clemency on the table at all," Napolitano said on NBC's "Meet The Press."

Paul said he doesn't think it's okay to leak information that could put American lives at risk but added that he feels Snowden uncovered improper activity by the federal government.

"Do I think that it's okay to leak secrets and give up national secrets and things that could endanger lives? I don't think that's okay, either," Paul said. "But I think the courts are now saying that what he revealed was something the government was doing was illegal."

Paul has criticized the broad federal surveillance efforts revealed by Snowden. He recently filed a class-action lawsuit against the government, and he's suggested that National Intelligence chief James Clapper lied to Congress about the government's data collection efforts.

Paul said Sunday that Snowden should probably face time in prison, but that so should Clapper.

"So I think, personally, [Snowden] probably would come home for some penalty of a few years in prison, which would be probably not unlike what James Clapper probably deserves for lying to Congress," Paul said, "and that maybe if they served in a prison cell together, we'd become further enlightened as a country over what we should and shouldn't do."

Updated at 1:57 p.m.