Sen. Rand PaulRandal (Rand) Howard PaulSunday shows — New impeachment phase dominates Rand Paul says Trump has 'every right' to withhold Ukraine aid over corruption Paul dismisses Bevin loss, touts 'red wave' in other Kentucky races MORE (Ky.) on Sunday voiced frustration with weeks of media attention on businessman Donald TrumpDonald John TrumpThis week: House kicks off public phase of impeachment inquiry Impeachment week: Trump probe hits crucial point Judd Gregg: The big, big and bigger problem 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.