WASHINGTON — Senator Rand Paul of Kentucky has not said if he plans to run for the Republican presidential nomination in 2016, but his supporters are already backing a bill in his state’s Legislature that would let him appear more than once on the ballot.

Mr. Paul, a first-term senator who is considered an early contender for his party’s presidential nomination, faces re-election in 2016. His aides have said they do not think that the state’s ban on officials’ seeking multiple positions would apply to Mr. Paul should he be nominated for a national office like president or vice president, because those are federal positions. But that did not stop them from asking State Senator Damon Thayer, a Republican and the Senate’s majority floor leader, to introduce a bill clarifying the matter.

“Federal law governs federal elections, and the Supreme Court has made it clear that states cannot impose additional qualifications beyond those in the Constitution,” Doug Stafford, a senior adviser to Mr. Paul, wrote by email. “We are not seeking to change the law, but rather to clarify that the Kentucky statute does not apply to federal elections.”

The bill cleared a committee in the Republican-controlled Senate on Wednesday and is expected to be passed by the full chamber in the next few days, said Jodi Whitaker, a spokeswoman for Mr. Thayer. Its chances are longer in the House, which is controlled by Democrats. Kentucky’s governor, Steven L. Beshear, is also a Democrat.