Trump has criticized the proposed deal, which the Justice Department has sued to stop. Legal experts have said the president's attacks on CNN could hobble his administration's case.
The president, who regularly assails mainstream media, has long criticized CNN, calling the network "fake news" and saying he no longer watches it, while lauding rival Fox News. His call for a boycott appeared to be a step up in his attacks.
"Great, and we should boycott Fake News CNN. Dealing with them is a total waste of time!," Trump wrote in a Twitter post.
Trump was responding to a post by his spokeswoman Sarah Sanders, who in her own post on Tuesday night praised reports that CNN would not attend an annual holiday party held at the White House for news media.
It was not immediately clear if Trump in his post was calling for a wider boycott against CNN or one by White House staff. Representatives for the White House did not immediately respond to a request for comment.
The network and its journalists have repeatedly defended CNN's work against previous presidential attacks.
The Department of Justice's challenge is unusual move given that pay TV and wireless company AT&T does not directly compete with TV show maker Time Warner. The department has said the lawsuit is a law enforcement decision, not a political one.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)