Opening a door to hedge his political bets, Sen. Rand Paul has asked the leader of the Kentucky Senate for legislation to ensure that Mr. Paul can run both for the White House and for re-election to the U.S. Senate in 2016, The Washington Times has learned.

“Yes, I am working on clarifying an ambiguous state law that Rand Paul believes is unconstitutional if it is interpreted to bar running for re-election to the Senate and for president at the same time,” Kentucky Senate Majority Leader Damon Thayer told The Times on Monday.

“The purpose of the bill will be to make clear that Rand Paul or anyone in a similar situation in Kentucky can run for both offices in the same year,” Mr. Thayer explained.

If things go Mr. Paul’s way, he could win the GOP presidential nomination, then run in the fall 2016 general election for the presidency and to retain his U.S. Senate seat. If he wins the presidency and the Senate re-election bid, he would relinquish his Senate seat.

If he loses the presidential election but wins the Senate re-election race, he would become a second-term U.S. senator from Kentucky.

Since winning his election in 2010, Mr. Paul has argued for creating term limits so members of Congress could serve a maximum of 12 years in each chamber.

Mr. Paul and his office did not immediately respond to requests for comment Monday. But in a recent C-SPAN “Newsmakers” program, Mr. Paul said he and his team were looking at the possibility of running for the Senate and the White House simultaneously.

“We just haven’t come to a conclusion yet,” he said at the time.

The situation has grown more complicated for Mr. Paul since his election in 2010. His fellow Kentucky Republican, Senate Majority Leader Mitch McConnell, faces a serious challenge from the political right in his own party.

If Mr. McConnell falls to the tea party candidate in the May primary or if a Democrat defeats Mr. McConnell in November, then Mr. Paul would become the senior U.S. senator from Kentucky. As such, he probably would become the recognized leader of his party in the state.

Fellow Republicans are counting on Mr. Paul to help them keep the state Senate from tipping to Democrats. The Kentucky state House already is controlled by Democrats.

Democrats have problems of their own in the state, including a sex scandal and accusations of a cover-up. Republicans think they have a shot at taking the House this fall, giving them two of the three power centers in state government. Gov. Steven L. Beshear is a Democrat.

A veteran Republican Party operative in Kentucky said privately that House Speaker Greg Stumbo, a Democrat, has told colleagues there is no way he would allow such a bill to go through his chamber.

“I’ve not spoken to the speaker about this and not heard publicly or privately what the Democrats in the House would do if Republicans passed it in the Senate,” Mr. Thayer said.

Mr. Stumbo did not return a phone call from The Times on Monday.

Mr. Paul isn’t the first federal candidate to seek two federal offices simultaneously.

Rep. Paul Ryan, Wisconsin Republican, in 2012, Sen. Joseph R. Biden, Delaware Democrat, in 2008, and Sen. Joe Lieberman, Connecticut Democrat, in 2000, all sought re-election while running for vice president.

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