Rupert Murdoch’s Fox News channel knew about Donald Trump’s illegal hush money payment to a pornographic film actor ahead of the 2016 election but killed the story because the media mogul wanted him to win, it was reported on Monday.

The Fox journalist Diana Falzone “had obtained proof” of Trump’s alleged extramarital affair with Stormy Daniels, as well as emails that showed his lawyer, Michael Cohen, planned to buy her silence through a non-disclosure agreement, according to the New Yorker.

But the report, a potentially huge scandal that could have damaged Trump at the polls, never saw the light of day. The Fox News executive Ken LaCorte reportedly told Falzone: “Good reporting, kiddo. But Rupert wants Donald Trump to win. So just let it go,” the New Yorker article says.

The magazine adds that LaCorte denied the comment, but one of Falzone’s colleagues confirmed having heard the account. Falzone was later demoted, sued Fox and reached a settlement that includes a non-disclosure agreement preventing her from speaking about the matter.

The symbiotic relationship between Trump’s White House and America’s most watched cable news network has become well established, with one amplifying the message of the other, for example by fanning fears of illegal immigration at the US-Mexico border. The president is a frequent Fox News viewer, often live-tweeting his reactions to the channel during his so-called “executive time”, and he has given it more than 40 interviews (compared with none for CNN).

Trump is known to speak regularly with a “brains trust” that includes the Fox News host Sean Hannity, who is given preferential access and widely suspected to have more influence with the world’s most powerful man than his own intelligence agencies. The New Yorker quotes Nicole Hemmer, author of Messengers of the Right, a history of the conservative media’s impact on American politics, as saying: “It’s the closest we’ve come to having state TV.”

The Wall Street Journal, also owned by Murdoch, revealed in January last year that Cohen had arranged the $130,000 transfer to Daniels weeks before the 2016 presidential election to stop her talking about the alleged affair with Trump in 2006.

The hush money payment has become a central focus of investigations into the president. Cohen pleaded guilty last year to a campaign finance violation related to the Daniels payout. Last week, testifying before Congress, Cohen produced what he claimed was a cheque from the Trump family paying him back.

On Monday, the New Yorker’s Jane Mayer published a major report on the quasi-merger between Trump and Fox News, suggesting the latter has power to shape government policy. It suggests that late last year Trump was poised to sign a spending bill to avert a partial government shutdown but was persuaded not to by Fox News pundits.

One of Mayer’s most significant findings relates to an effort in 2017 by Trump to pressure Gary Cohn, then director of the National Economic Council, to pressure the justice department to thwart AT&T’s $85bn acquisition of Time Warner.

The president reportedly summoned Cohn and Trump’s then chief of staff John Kelly into the Oval Office and said to Kelly: “I’ve been telling Cohn to get this lawsuit filed and nothing’s happened! I’ve mentioned it 50 times. And nothing’s happened. I want to make sure it’s filed. I want that deal blocked.”

The New Yorker reports: “Cohn, a former president of Goldman Sachs, evidently understood that it would be highly improper for a president to use the justice department to undermine two of the most powerful companies in the country as punishment for unfavorable news coverage, and as a reward for a competing news organization that boosted him.

“According to the source, as Cohn walked out of the meeting he told Kelly, ‘Don’t you fucking dare call the justice department. We are not going to do business that way.’”

The claim prompted sharp criticism. Ted Lieu, a Democratic congressman, tweeted: “If this Jane Mayer article is accurate, it means @realDonaldTrump engaged in abuse of power.”

George Conway, a lawyer and Trump critic who is also married to the White House counselor Kellyanne Conway, tweeted: “If proven, such an attempt to use presidential authority to seek retribution for the exercise of First Amendment rights would unquestionably be grounds for impeachment.”

The AT&T/ Time Warner deal eventually went ahead after the justice department lost in court.

Mayer writes that a “a direct pipeline” has been established between the Oval Office and Murdoch. “Multiple sources told me that Murdoch and Trump often talk on the phone. A former aide to Trump, who has been in the Oval Office when Murdoch has called, says, ‘It’s two men who’ve known each other for a very long time having frank conversations. The president certainly doesn’t kowtow to Murdoch, but Murdoch also doesn’t to him.’”

Upon request for comment, a Fox News spokesperson referred the Guardian to a statement released last year by Noah Kotch, then editor-in-chief and vice-president of Fox News Digital but now no longer at the company.

It said: “Like many other outlets, we were working to report the story of Stephanie Clifford’s account in October 2016 about then presidential candidate Donald Trump and a possible payment by Trump lawyer Michael Cohen. In doing our due diligence, we were unable to verify all of the facts and publish a story.”