"I would absolutely not run unless it were to win," the Kentucky Republican said on "Fox News Sunday." "Points have been made, and we we will continue to make points. But I think the country is really ready for the narrative coming -- the Libertarian Republican narrative."
Voters want a "different face," he said.
In order to expand the party's reach, Paul believes the GOP should embrace candidates who are willing to push a less aggressive foreign policy, comprehensive immigration reform and less punitive measures on first offenders of non-violent drug possession.
"We're doing fine in congressional seats, but we're becoming less and less of a national party," Paul said.
Paul garnered 10 percent in a recent PPP poll on 2016 (pdf), just below Chris Christie, Jeb Bush and Mike Huckabee, almost four years out from the election.