"We are in active discussions with the DOJ", John J. Stephens, chief financial officer for AT&T, said at a Wells Fargo conference. "And likewise I have never offered to sell CNN", he said.
A lot of different options are on the table for how to proceed, Justice Department officials said.
The government's reservations about the deal stem from the effects of combining AT&T's distribution platforms, including satellite television provider DirecTV, and the wide catalog of content under the Time Warner umbrella, such as Turner Broadcasting, CNN's parent company. He added, "I have never offered to sell it".
Shares of Time Warner fell 1.4 percent on Thursday to $87.27 in heavy volume.
Trump's concerns echo those expressed by many critics of the proposed deal who think too much consolidation in the media and telecom industries is ultimately bad for both.
The Justice Department has been reviewing the merger since early this year. The previous administration settled a similar tie-up between a pay-TV company and an entertainment giant, the acquisition of NBCUniversal by Comcast Corp., by imposing conditions. Without an agreement, the Justice Department would sue to block the merger - with a lawsuit possibly coming as soon as next week, one of the people said.
"The Department is committed to carrying out its duties in accordance with the laws and the facts", the agency said. "Beyond that, the Department does not comment on any pending investigation".
The DOJ does not comment on ongoing matters and has declined comment on the AT&T-Time Warner deal as well.More news: Obama heads to downtown Chicago for jury duty
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Nevertheless, the Justice Department says it flatly denied the proposal for AT&T to sell CNN, insisting it wouldn't necessarily resolve their concerns.
Stephenson wants to pair all the programming those divisions produce with advertising and other services to create new sources of revenue. Many criticized the move, stating it would lead to a concentration of media power. "I have no reason to believe" the Trump theory, he said. Delrahim told senators during his confirmation process that politics has no role in antitrust reviews.
The deal is valued at $85 billion and had been expected to close by the end of the year.
Thursday's reports also touched off speculation that the Justice Department's insistence on a divestiture could have political overtones, after Trump's outspoken criticism of CNN's coverage of his administration.
Raj Shah, a White House spokesman, said in a separate statement that Trump "did not speak with the Attorney General about this matter, and no White House official was authorized speak with the Department of Justice on this matter".
However, he stated that the company was unconcerned with the amount of time spent on the issue.
Democratic lawmakers and advocacy groups have been ringing alarm bells about the potential for political interference in what's supposed to be an independent antitrust review of the deal.