AT&T has "no intention" of selling CNN despite the Justice Department's demand the company sell it in order to approve the Time Warner acquisition, according to CEO and chairman Randall Stephenson.

"Until now, we've never commented on our discussions with the DOJ," Stephenson said in a statement. "But given DOJ's statement this afternoon, it's important to set the record straight. Throughout this process, I have never offered to sell CNN and have no intention of doing so."

Sources told CNBC that the Justice Department wants AT&T to sell Turner Broadcasting, which includes CNN, or DirecTV as condition for approval of the $85 billion AT&T-Time Warner deal.

In addition, DOJ sources told NBC News AT&T offered selling CNN during a meeting on Monday regarding the proposed merger. The DOJ's Antitrust Division "flatly rejected it" because it would not solve potential anti-competition issues. Justice Department officials told NBC News there are multiple ways to solve issues regarding the AT&T-Time Warner deal, but selling CNN would not resolve concerns.

"The Department is committed to carrying out its duties in accordance with the laws and the facts," a DOJ spokesperson said in response to Stephenson's statement. "Beyond that, the Department does not comment on any pending investigation."

Time Warner shares were down 6 percent after the reports. AT&T's stock was up 1 percent.

President Donald Trump has repeatedly criticized CNN as fake news on his social media Twitter account in the past year.

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The company previously said it expected the deal to close by the end of 2017.

When asked about the deal earlier Wednesday at the Wells Fargo Media and Telecom Conference in New York, AT&T Chief Financial Officer John Stephens said:

"We are in active discussions with the [Department of Justice]. Those are continuing on. I can't comment on those discussions, but with those discussions, I can now say that the timing of the closing of the deal is now uncertain."

Stephens said the AT&T acquisition of Time Warner is a "vertical integration" merger across industries. He noted that the government has not blocked a "vertical" deal in more than 40 years.

AT&T announced the cash and stock deal to acquire Time Warner in October 2016.

Time Warner shares dropped 4 percent on Nov. 2 after The Wall Street Journal reported that the Justice Department's antitrust division was preparing for litigation in case it decided to sue to block the deal.

The Financial Times first reported on Wednesday that the Justice Department told AT&T and Time Warner it must sell CNN. The New York Times later reported that either CNN or DirecTV must be sold.

—CNBC's Andrew Ross Sorkin contributed to this report.