"Is John Brennan monetizing his security clearance? Is John Brennan making millions of dollars divulging secrets to the mainstream media with his attacks on @realDonaldTrump," the Kentucky Republican tweeted Monday morning. "Today I will meet with the President and I will ask him to revoke John Brennan's security clearance."

Brennan, who was CIA director under President Barack Obama, now works as a senior national security and intelligence analyst for NBC News and MSNBC. Brennan has been highly critical of Trump.

Most recently, he lambasted Trump's meeting with Russian President Vladimir Putin last week, calling it "nothing short of treasonous" in a tweet.

Paul's request comes after Fox News host Tucker Carlson said last week that Brennan still had a security clearance despite not working for the federal government anymore.