Rep. Ron Paul (R-Texas) said he hasn't given much thought to a presidential campaign as an Independent, but called laws making a third-party bid more difficult a "shame."

Paul, who announced that he wouldn't seek reelection to his House seat in order to focus on his presidential campaign, hinted at the possibility of a third-party campaign for the White House if he doesn't win the GOP nomination.

"Some states preclude it; if you sign on and become a Republican candidate, then the law says you can’t become an Independent," Paul said on the Fox Business Network. "I have not really looked into that, because I have not been thinking along those lines, but I think it would be a shame if you couldn’t do that."

The Texas congressman's campaign is seen as a relative long-shot bid for the presidency, though Paul commands a loyal and intense base of supporters who've helped him build a small political organization.

Whether that organization could translate into a credible third-party campaign is unclear. If nothing else, it could threaten to siphon votes from the eventual nominee in a way that Democrats alleged Green Party candidate Ralph Nader had done in 2000.

Paul decried, though, the lack of ballot access for third-party candidates as one of the "shortcomings" in U.S. politics, but said he'd continue to voice his libertarian strain of politics, regardless of his membership in the House.