Updated 6:31 p.m. ET, 3/6/2014
Washington (CNN) - A top Kentucky legislative leader allied with GOP Sen. Rand Paul filed a bill Thursday pushing for changes that would allow the libertarian-leaning lawmaker to simultaneously seek both the presidency and re-election to his Senate seat in 2016.
Republican state Senate Majority Leader Damon Thayer's bill says Kentucky's law prohibiting running for two offices at the same time is meant to apply only to state-level offices - not federal offices such as the presidency, the U.S. Senate or the U.S. House.
The proposed legislation states that Kentucky's current law, "...shall not prevent a candidate's name from appearing on a voting machine or absentee ballot twice if one (1) or both of the offices sought is a federal office."
"Senator Paul is very popular here, and I personally don't want to deny Kentuckians the chance to vote for or against one of their own for the Senate if he's also nominated for the presidency," Thayer told CNN on Tuesday.
A number of other states let politicians run for the House or Senate while also running for the White House, Thayer noted.
"It's not fair to Senator Paul if he can't do the same," he said. "Why should Kentucky be any different when it comes to one of their own running for president?"
Thayer told CNN he has spoken "in general terms" to Paul about potential changes to Kentucky's law.
"I'm a strong supporter of Paul's," Thayer said. "I hope he runs for president."
Doug Stafford, a political adviser for Paul, said, "We are not seeking to change the law, but rather to clarify that the Kentucky statute does not apply to federal elections."
Even if Kentucky's GOP-controlled Senate passes changes to the current state law, it appears unlikely those changes could pass Kentucky's Democratic-controlled House of Representatives or win the approval of Democratic Gov. Steve Beshear.
House Speaker Greg Stumbo "believes people ought to run for one office at a time," said Brian Wilkerson, a spokesman for the speaker.
Stumbo told reporters last Friday that he believes running for two offices at once would set "a bad precedent."
A Kentucky House Democratic staffer told CNN it is "very unlikely" changes being contemplated by the GOP-controlled Senate will pass both chambers of the state Legislature.
Paul, a tea party favorite, is considered a likely contender for the 2016 Republican presidential nomination. If that bid doesn't pan out, a Senate re-election victory would allow him to maintain his foothold on Capitol Hill for another six years, starting in January 2017.
Several members of recent presidential tickets have essentially hedged their political bets by running for re-election while simultaneously pursuing higher office.
Wisconsin Rep. Paul Ryan ran for re-election to his seat in 2012 while serving as the GOP vice presidential nominee on Mitt Romney's ticket. Then-Sen. Joe Biden also ran for re-election in Delaware while simultaneously serving as then-Sen. Barack Obama's running mate in 2008.
In 2000, Joe Lieberman was re-elected to his Senate seat in Connecticut while losing his bid for the vice presidency when he and Vice President Al Gore, the Democratic presidential nominee, narrowly lost the election to George W. Bush and Dick Cheney.
CNN's Alison Harding, Paul Steinhauser and Dana Davidsen contributed to this report