Prosecutors in New York have spoken to the CEO of the company that publishes the tabloid National Enquirer as part of the district attorney's investigation into Donald Trump's alleged "hush money" payments to women with whom he has had affairs, according to CNN.

Their meeting with David Pecker, who heads American Media Inc, which publishes the tabloid, could lead to his appearance as a key witness in potential hearings to determine whether Mr Trump broke any state laws by negotiating payments to adult film star Stormy Daniels through the president's former attorney Michael Cohen in an effort to "silence" her story of an affair.

Prosecutors also believe Mr Pecker and AMI helped bury a story of an alleged affair between Mr Trump and former Playboy model Karen McDougal. The company paid Ms McDougal $150,000 for the rights to the story, which it published in part.

Mr Trump has denied the affairs.

According to statements between AMI and prosecutors, Mr Pecker met Mr Trump during his campaign in August 2015 to discuss whether the candidate was aware of any damaging stories that could surface during the campaign and potentially threaten his bid for the White House.

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In October 2016, a representative for Ms Daniels contacted AMI with on-record allegations of her affair with Mr Trump. It was then that Mr Pecker alerted Cohen to the allegations. According to court filings, Cohen arranged $130,000 for Ms Daniels for her "silence".

That payment allegedly was delayed, and Ms Daniels threatened to take her story to another publication. According to court documents, Mr Pecker told Cohen that he needed to make the payment or "or it could look awfully bad for everyone".

Cohen was allegedly reimbursed by the Trump Organisation following his payment to Ms Daniels.

According to prosecutors, the Trump Organisation paid Cohen $420,000, then falsely recorded those payments as legal expenses.

The district attorney has issued a subpoena for the president's tax filings, which the US Supreme Court could determine must be released after Mr Trump and his attorneys have made repeated attempts to stop or delay the case, citing presidential immunity.