Sen. Rand PaulRandal (Rand) Howard PaulLexington mayor launches bid for Congress Trump-free Kennedy Center Honors avoids politics Meet the Iran hawk who could be Trump's next secretary of State MORE (Ky.) on Sunday voiced frustration with weeks of media attention on businessman Donald TrumpDonald John TrumpHouse Democrat slams Donald Trump Jr. for ‘serious case of amnesia’ after testimony Skier Lindsey Vonn: I don’t want to represent Trump at Olympics Poll: 4 in 10 Republicans think senior Trump advisers had improper dealings with Russia MORE, a fellow Republican presidential rival, while suggesting his own campaign is rolling along.

"I think if you give any candidate about a billion dollars worth of free advertising that might help them get their message out," Paul said on CBS's "Face the Nation."

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Trump has dominated headlines since launching his White House bid in mid-June, stemming from his controversial remarks on immigrants from Mexico, fizzled business ties and intra-party jabbing.

The celebrity real estate developer has also skyrocketed to the top of recent polls, putting him in GOP debates starting next week.

Regarding his own White House prospects, Paul acknowledged that his campaign hasn't "gotten quite the same attention recently," but said, "I think we're still doing quite well."

Paul was among the leading potential GOP candidates in several polls earlier this year, but currently trails more than a handful of other candidates in the Real Clear Politics average, which puts him at seventh.

The libertarian-leaning lawmaker noted his efforts to bring his Republican campaign to areas like Detroit, southern Chicago and Ferguson, Mo., and the need for the GOP to attract black voters.

"I am trying to say, you know what, I am a different kind of Republican and we need a more diverse Republican Party," Paul said on CBS.