"I have no intention doing that. That doesn't make sense to me to even think about it, let alone plan to do that," Paul told "Fox News Sunday."
Asked why, Paul responded: "Because I don't want to do it. That's the reason."
But, that doesn't mean he'd support Mitt Romney or Herman Cain:
But Paul said that if he's not the nominee, he's not certain that he would support the GOP nominee.
"Probably not unless I get to talk to them and find out what they believe in. But if they believe on expanding the wars, if they don't believe in looking at the Federal Reserve; if they don't believe in real cuts, if they don't believe in deregulation and better tax system, it would defy everything I believe in," Paul said.