Sen. Rand PaulRandal (Rand) Howard PaulNSA spying program overcomes key Senate hurdle Fix what we’ve got and make Medicare right this year Despite amnesty, DACA bill favors American wage-earners MORE (R-Ky.) said Friday he would be honored to join the Republican ticket as the vice presidential nominee, just one day after he endorsed Mitt Romney's campaign.

"A year, year and a half ago, I was a physician in a small town, and it would be a great honor to be considered as a vice president for the Republican Party," Paul told CNN. "I think that would be something that anybody who said otherwise would not be being truthful."

But the first term senator said he had not discussed joining the ticket with Romney, whose vice presidential search is already underway. 

Paul would be an unconventional choice for Romney; Kentucky, his home state, is expected to vote solidly Republican in November and his Tea Party brand of libertarian politics break with the Republican nominee on some key issues. But Paul is extremely popular with elements of the conservative base, and could lean on his father — Rep. Ron Paul's (R-Tex.) — extensive national fundraising network cultivated during his bid for the White House.

On Thursday night, Paul told Fox News that while his father would remain his "first pick" for the Republican nomination, he recognized that Romney would be the nominee and felt a "kinship" with the former Massachusetts governor on several issues.

"My first choice had always been my father. I campaigned for him when I was 11 years old. He's still my first pick," Paul said. "But now that the nominating process is over, tonight I'm happy to announce that I'm going to be supporting Gov. Mitt Romney."