Sen. Rand Paul (R-KY) on Saturday denied having made a secret deal to be on the ticket with presumptive GOP presidential candidate Mitt Romney.

"You know, I would say what I have said before," he told CNN's Don Lemon after being asked if he would consider running for vice president. "I think it would be an honor. And I think anybody who said they wouldn't be honored by it isn't being honest. A year, a year and a half ago, I was a physician in a small town. And to be honored -- 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."

In February, Rick Santorum accused Ron Paul of having a backroom, running-mate deal with Romney to see his son on the 2012 ticket. An analysis by Think Progress found that Ron Paul never attacked Romney during the 20 televised debates and the Washington Post reported that Romney's aides have quietly been in touch with Ron Paul during the campaign.

Rand endorsed Romney for president on Saturday. But he denied there was any deal between his father, who is still technically running for the GOP nomination, and Romney.

"No, no real secret deal," he said. "I always tell people, if there's a secret deal, it's so secret that I don't know about it. But I would say that my dad's supporters are very, very independent. Many conservatives and libertarians are independent people. And I don't pretend to speak for them. They make up their own minds. Some of them might be influenced to hear the governor out, listen to the areas of common interest. They're not going to agree with everything Governor Romney stands for."

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[Image via Gage Skidmore, Creative Commons licensed]