In contrast to Trump's pro-business position overall, he remains against a merger of the biggest traditional pay TV provider, AT&T, and one of biggest suppliers of TV and movie programming, Time Warner.
But many analysts are wondering if all this really centers on CNN.
Trump had repeatedly criticized CNN for its coverage of his presidential campaign -- in addition to be angry at much of TV/press election coverage overall, including The New York Times, The Washington Post, Fox News Channel.
Unlike other business industries -- such as car manufacturers -- focusing on the media isn't about protecting U.S. jobs. Trump believes -- as do many liberal-minded political figures -- that an AT&T-Time Warner deal would concentrate too much media in one company.
That may have been the case two decades ago, but not now. Big business/new media entrepreneur Mark Cuban strongly disagrees with Trump, saying the AT&T/Time Warner has more to fear from Google, Facebook, Netflix, and others -- new digital media players who command a healthy share of advertising dollars — and U.S. consumers' media time.
What could AT&T do? Craig Moffett media analyst of MoffettNathanson says if AT&T could sell CNN to get the deal to the finish line, perhaps the company would do that.
CNN isn’t alone. Trump also blames other big media -- Comcast/NBCUniversal during the campaign season -- especially in releasing the 2005 audio tape from NBCU’s syndicated “Access Hollywood” show, where he made sexually disparaging and predatory comments about women.
Much of the decision around AT&T/Time Warner depends on where priorities for the Department of Justice and/or the Federal Communication Commission will be once Trump assumes office.
A bigger issue is whether there will be any consistent policy around other media issues in general -- for example, mergers featuring traditional media or new digital media companies.
One thing is certain Trump will continue to voice his opinions on his favorite popular digital media platform -- Twitter -- a company that has been the subject of constant merger talks.
When and if that happens, one wonders where the Trump sentiment will land from that 140-character missive. Perhaps sthis will be just another conflict of interest the president-elect will need to resolve -- or avoid.