There’s still time for Kentucky Sen. Rand Paul to heed the calls of #NeverTrump voters urging him to run for the Libertarian Party presidential nomination, but the window is closing.

Carla Howell, political director of the National Libertarian Party, said Wednesday that would-be nominees would need to capture 10 percent of the convention delegates by May 28 in order to participate in that evening’s presidential debate.

The nominee will be chosen May 29 at the Libertarian Party National Convention in Orlando, Florida. Prior to that, candidates must register as Libertarian, file with the Federal Elections Commission and create a presidential campaign website, she said.

Another name being floated as a possible last-minute entrant is Mr. Paul’s father, former Texas Rep. Ron Paul.

“It is not too late, especially for someone like [Ron Paul] who is well-known and liked in the party,” Ms. Howell said in an email.

Seventeen candidates are already vying for the Libertarian Party presidential nomination, but Rand Paul has been at the center of third-party speculation for months, especially since real-estate mogul Donald Trump effectively captured the Republican nomination by winning Tuesday’s Indiana primary.

“If the orange one is the Republican nominee will you please run 3rd party Rand Paul?” asked Jeremy Taylor in a post this week on Mr. Paul’s Facebook page.

One problem for Mr. Paul is that he’s running for Senate re-election and would have to give up his seat in order to run as the Libertarian presidential candidate.

He indicated in September that he would sign a pledge not to run as a third-party candidate and also urged Mr. Trump to do so, saying it could “give us another Clinton” in the White House, referring to Democratic front-runner Hillary Clinton.

Former New Mexico Gov. Gary Johnson, the Libertarian Party’s presidential candidate in 2012, has urged Republicans to cross over and support his 2016 campaign for the nomination, describing himself as the only small-government candidate left in the race.

“Gary Johnson’s fine, but I would be much happier to vote for Rand Paul,” said Krista Kafer, a Denver Post columnist and #NeverTrump stalwart. “He’s terrific.”

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