The dispute is the latest twist in a deal which took on broader political significance immediately after its inception in October 2016.
AT&T chief financial officer John Stephens told a conference in NY "there are all kinds of benefits" to the combination and noted that the government has not blocked this kind of vertical tie-up in decades.
Some sources say AT&T floated the possibility of selling CNN or other assets.
On Sunday, White House adviser Kellyanne Conway told CNN that the White House would not interfere with the merger review. The official, who was not authorized to discuss the matter publicly, said the department rejected that offer as insufficient to resolve its concerns, which it did not specify. As president, Trump has often blasted CNN for its coverage of him and his administration, disparaging it and its reporters as "fake news".
"Until now, we've never commented on our discussions with the DOJ", Stephenson said in a statement.
AT&T may choose to force the DOJ's hand by moving to close the deal, which could trigger a court fight.
Shares of AT&T climbed 1.15 per cent on Wednesday on the New York Stock Exchange, while Time Warner tumbled 6.51 per cent. Transactions like Comcast's acquisition of NBCUniversal in 2011 are routinely approved with conditions attached.
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One Justice Department source told CNBC that the idea of shedding CNN to complete the deal originated with AT&T, a contention that drew an immediate denial from the Dallas-based firm.
A CNN sale reportedly is at the heart of pressure the DOJ is putting on AT&T in order for its blockbuster deal to merge with Time Warner to win federal approval.
"We think AT&T's merger approval chances would be further improved if there's meaningful criticism in the coming days of Trump possibly using antitrust law to target CNN, and either the president or DOJ decide a court challenge isn't worth it, especially with DOJ likely to lose the court case", Gallant wrote.
"For over 40 years, vertical mergers like this one have always been approved because they benefit consumers without removing any competitors from the market", AT&T said last week. "Beyond that, the department does not comment on any pending investigation".
But as a candidate, President Trump publicly vowed to block the transaction.
Delrahim was subsequently nominated by U.S. President Donald Trump to head the Justice Department's antitrust division and was confirmed in September.
The New York Times explains that these "behavioral remedies" are typical in vertical mergers, but "t$3 he Justice Department's demands for divestitures would be a major change in antitrust policy".