(CNN) - A day after endorsing Mitt Romney, Sen. Rand Paul said it would be an honor to run alongside the presumptive GOP presidential nominee.
"A year, year and a half ago, I was a physician in a small town," Paul, the junior Republican senator from Kentucky, told CNN's Don Lemon. "And it would be a great honor to be considered as a vice president for the Republican Party. I think that would be something that anybody who said otherwise would not be being truthful."
Paul, who on Thursday came out in support of Romney, said on CNN he had not discussed with the candidate the prospect of joining the GOP ticket.
Paul, a tea party favorite and son of presidential candidate Ron Paul, said his father "has always been my first choice," but that the nominating process favored Romney.
"The nomination is now done and Romney has achieved the amount of delegates necessary to be the nominee," Paul said. "Those are just facts. And I've decided to endorse Romney after meeting with him and talking about a lot of areas that we actually do have common ground on."
His announcement came one day after his father acknowledged he would not become the Republican nominee, despite maintaining for months that he would stay in the fight for the White House.
Ron Paul ended his official campaign events weeks ago, but he's still technically a presidential candidate and will have delegates at the Republican National Convention in August.
CNN's Ashley Killough contributed to this report.