"I'm not going to deny that I'm interested," Paul told ABC's Jonathan Karl in a segment called "Spinners and Winners."
Paul, who was first elected to the Senate in 2010 and has been frequently mentioned as a possible presidential candidate, said he hasn't made a final decision yet on whether to run in 2016.
"I think it's a little too early," he said. "We'll see what happens."
After a bruising Nov. 6 election, Paul told ABC the Republican Party needs to change some of its stances, although not what he called the party's core message of encouraging economic growth to generate government revenue.
"I think we have to go in a different direction because we're just not winning, and we have to think about some different ideas," Paul told ABC.
Some of those different ideas include allowing states to make decisions on the legalization of marijuana and taking a less hard-line stance on immigration. Paul said he still favors border security but would be open to looking at paths to citizenship for people who have been in the country illegally for decades.
"We have to let people know, Hispanics in particular, we're not putting you on a bus and shipping you home," Paul said.
The Republican Party, Paul noted, is losing the Hispanic vote, a growing segment of the voting population.
With the retirement of his father, U.S. Rep. Ron Paul of Texas, many are looking to the Bowling Green eye surgeon to take up his father's Libertarian-leaning agenda. The elder Paul ran for president three times, most recently in the 2012 Republican primary.
In the ABC News interview, Rand Paul said his father has helped the Republican Party by bringing new ideas and new people into the political process.
"He's grown the party in a tremendous way," Paul said.
More Nation & World Headlines
Tunisian democracy group wins Nobel Peace Prize 2:46 a.m. 1 dead, 3 wounded in Arizona university shooting 4:05 a.m. GOP turns to reluctant Paul Ryan for speaker post Donald Trump says Bowe Bergdahl should have been executed NASA spacecraft finds blue sky, red ice at Pluto ‘Dateline NBC’ gathers Bill Cosby accusers for special ‘Lucky’ pig gets new home after fall onto Colorado highway Greek town to test new driverless buses
Our new comment system is not supported in IE 7. Please upgrade your browser here.