Asked by NBC's Jay Leno whether he had any advice for his son, who is considering running in 2016, the elder Paul urged caution.
"I would say be very cautious. You could get elected. That's the risk in running for politics," he said.
He said he had never talked to his son about running, and hadn't consulted with him much about his underdog bid for Senate in 2010, when a late surge in grassroots support catapulted him to an improbable win over his establishment-backed GOP primary challenger and a well-funded Democratic opponent.
Ron Paul said his son's success that year "surprised" him.
"I think when he ran for Senate he sort of surprised me, and he didn't do it with a serious consultation with me, and I didn't think he would do that well," he said.
"He did exceptionally well," he added, noting that most of the grassroots intensity on Paul's side came from Tea Party groups, which played a central role in reshaping the landscape of the House and Senate in 2010.