Former White House Chief of Staff Reince Priebus said he wasn't sure how true some of the claims were about a data analytics firm and its influence on the U.S. presidential election.

Cambridge Analytica — a firm publicly associated with President Donald Trump's campaign — is said to have collected private information from Facebook profiles of more than 50 million users without their permission, according to reports from The New York Times and the Observer.

The Times said the firm paid to acquire the data through someone claiming to be an academic researcher. It added that the breach allowed Cambridge Analytica to exploit the private social media activity of a huge swath of the American electorate and develop techniques that underpinned its work on the Trump campaign in 2016.

Additionally, a new report from Channel 4 in the U.K. shows Cambridge Analytica CEO Alexander Nix claiming his company ran all the digital operations for the Trump campaign.

"We did all the research, all the data, all the analytics, all the targeting, we ran all the digital campaign, the television campaign and our data informed all the strategy," Nix was recorded saying during the news channel's undercover investigation.

Priebus, however, cast down on those assertions.

"I don't know how true some of these claims are," Priebus told CNBC in Hong Kong at the Credit Suisse Asian Investment Conference. "Certainly from the Republican National Committee standpoint, which was the data firm of the Trump campaign, which is what we built at the RNC, we didn't use Cambridge. So I don't know how true any of these claims are."

"I don't know if their folks are bragging that they were doing things that they weren't. Maybe they were doing things, I don't know," he added.

Priebus chaired the RNC throughout the last U.S. presidential election.

In a statement on Tuesday, Cambridge Analytica said it had suspended Nix immediately, "pending a full, independent investigation."

Cambridge has denied the allegations made in the Times' report.

When asked about the ties Cambridge had with the Trump campaign, Priebus said, "We just weren't relying on them."

"So maybe, initially, they played ball with the campaign but it wasn't soon after we merged with the Trump campaign that they went onto full-blown RNC data," he said. "So I think they themselves in November-December of last year said the same thing — that they were using RNC data, not Cambridge Analytica."

On Tuesday, Facebook released a statement saying the "entire company is outraged" that data from 50 million accounts were allegedly deceptively used by the analytics firm. Reports said the Federal Trade Commission was investigating the tech giant for a possible violation of a consent decree it signed with the agency in 2011.

"I'm anxious to hear what the story is, but as far as we're concerned, RNC data was the driver," Priebus added. "We built something very special — nothing's like our data. It's the best there is and that's what got President Trump, at least on that piece of campaign, to where he was."

— CNBC's Anita Balakrishnan contributed to this report.