Dylan Lovan, Associated Press
U.S. Sen Rand Paul, R-Ky., speaks with a supporter after a town hall meeting in Murray, Ky. on Wednesday, Jan. 11, 2012. Paul, a Republican from Bowling Green, said he has been impressed by the campaign of his father, Rep. Ron Paul of Texas, and said he believes the Republican presidential race is now between his dad and former Massachusetts Gov. Mitt Romney.

LOUISVILLE, Ky. — U.S. Sen. Rand Paul said Thursday he hasn't thought much about a vice presidential bid this year as his father challenges Republican front-runner Mitt Romney in the presidential primaries, but he also did not rule out the possibility.

Paul, speaking Thursday morning in Louisville, said he's "seen the chatter on the Internet" about the possibility of being tapped as the GOP nominee's running mate. But he said for now he is focused on helping U.S. Rep. Ron Paul's campaign for the GOP nomination.

"I haven't really considered it yet," Rand Paul said. "I'm focused on trying to help my dad."

The Republican from Bowling Green made his comments Thursday morning at the St. Matthews Community Center in Louisville after saying his office would give $500,000 in office funds back to the U.S. Treasury.

Ron Paul of Texas finished second in the New Hampshire Republican presidential primary. Rand Paul said the presidential race is now between his father and Romney, the former Massachusetts governor who won the Iowa caucuses and New Hampshire primary. Romney, Ron Paul and other Republican candidates are now working in South Carolina, which votes on Jan. 21.

None of the remaining presidential candidates — including Romney, Paul, former House Speaker Newt Gingrich of Georgia, ex-Sen. Rick Santorum of Pennsylvania, one-time Utah Gov. Jon Huntsman and Texas Gov. Rick Perry — has talked publicly about who they would select as a running mate.

And Rand Paul said no one has approached him about it.

"I haven't had personal discussions with any presidential candidate, other than my dad, and that's not a consideration with my dad," he said.

The senator said that his father and Romney are the top two remaining candidates for the GOP nomination, and that either could defeat President Barack Obama in the fall.

"We think it's essentially a two-man race," Paul said.

Winning South Carolina is about taking advantage of the second-place showing in New Hampshire and capitalizing on a "bounce" from the strong finish "to show that there's an upper tier and a lower tier and that Ron Paul is in the upper tier, which we're excited about," Rand Paul said.

"Hopefully, when you get to S.C., you want to become the viable alternative to Gov. Romney," Rand Paul said. "If you do, maybe people will coalesce around your candidacy and you can challenge Gov. Romney. Gov. Romney is still the guy to beat."

Paul's appearance in Louisville came as part of a series of meetings across Kentucky. At the Louisville appearance, Paul announced his office would give $500,000 to the U.S. Treasury from his office's $3 million budget. Paul said the funds weren't needed as he economized the office's spending.

While many congressional and senatorial offices return money to the Treasury, Paul said he knows of no other office that has returned as much in a single payment.

"It's what ought to happen throughout government," Paul said. "You could reduce government by 10 percent and not cut one service."

Associated Press reporter Brett Barrouquere is on Twitter: http://twitter.com/BBarrouquereAP