Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) suggested Thursday that the National Security Agency might have records on President Obama's phone calls.

In an interview with Bloomberg, Paul noted that the NSA has acknowledged that it collects data, such as phone numbers, call times and call durations, on all U.S. phone calls.

"My question is, are they tapping the president's phone, also?" Paul asked on Bloomberg's "Political Capital." "He's got a cellphone … I mean, think about it."

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Paul said he was making the comment a "bit facetiously" but that the court orders authorizing the NSA surveillance are "so expansive and without limit and nonspecific that they apply to all cellphones."

"So conceivably, the NSA could be spying on the president's phone,” Paul said.

"Now, I think he's encrypted. He's protecting himself from his own spy agency because he's got his phone encrypted. But do the rest of Americans have to get encrypted phones?"

Paul is a co-sponsor of a bill with Sens. Ron Wyden (D-Ore.), Mark Udall (D-Colo.) and Richard Blumenthal (D-Conn.) that would end the NSA's bulk phone record collection program.

The phone record collection was one of the most controversial revelations from the leaks by Edward Snowden.

In a separate interview on Fox News Thursday, Paul demanded that Obama respond to allegations that the NSA spied on the Vatican as cardinals met to select a new pope earlier this year.

The NSA has categorically denied targeting the Vatican, which was first reported in an Italian magazine.

"The NSA also says collecting bulk data on Americans is not spying," Paul said. "So you have to parse their words."