Though the deal reportedly never came together, the Times' report sheds new light on a recorded conversation released by Cohen's attorney.
So Trump and Cohen cooked up a plot to buy the whole lot of gossip -including "stories about Mr. Trump's marital woes and lawsuits; related story notes and lists of sensitive sources; some tips about alleged affairs; and minutia, like allegations of unscrupulous golfing" - from the Enquirer.
"It's all the stuff - all the stuff, because you never know", Cohen could be heard saying on a recording that's already received attention.
Several U.S. media outlets including the Wall Street Journal reported this week that Pecker was granted immunity by federal prosecutors in connection with an investigation into payments made during the 2016 U.S. presidential campaign to two women who claimed to have previously had affairs with then-candidate Donald Trump.
Postmedia CEO Paul Godfrey thanked Pecker for his service since being appointed to the board of directors in October, 2016.
This is how the National Enquirer covers Trump. Her story was not published, the broadcaster said.
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The payments were directed by Trump and amounted to illegal campaign contributions, according to Cohen.
Mr. Cohen, those people said, was hearing rumors that Mr. Pecker might leave American Media for Time magazine - a title Mr. Pecker is known to have dreams of running.
The Times based their report on insiders who knew about the discussions but would speak about them only on condition of anonymity, so as not to be drawn into the legal cases swirling around both Cohen and the president. "Those individuals are the ones who would have knowledge about what, if anything, the campaign at the highest, or lowest, or any level in between had on this issue".
American Media owns the National Enquirer and allegedly made "catch and kill" deals that helped keep the alleged affairs out of the tabloid, Vanity Fair first reported.
Several former American Media staffers also told the Times that the stories would have put the Enquirer in an excellent position to dominate coverage of the president's past scandals.