Republican presidential candidate Ron Paul rejected a suggestion that GOP frontrunner Mitt Romney would ask his son, U.S. Sen. Rand Paul, R-Ky., to serve as his running mate.

There has been growing speculation that the Romney and Paul campaigns have been cooperating with a possible offer of the vice presidency to Kentucky’s junior Senator down the road. When WFPL asked Sen. Paul about the prospect, he said “it would be an honor to be considered” and didn’t shut the door the the rumors.

But Congressman Paul dismissed the speculation after GOP presidential candidate Rick Santorum suggested Paul and Romney were colluding.

“I think the media has fed on that because they keep saying ‘Is there a deal, is there a deal?’” Paul told Politico. “Obviously not. He wouldn’t do it, I wouldn’t’ do it.”

In a recent interview, Romney has also downplayed the rumors.