US federal prosecutors have reportedly granted immunity to the head of the company that publishes the National Enquirer as they investigate hush money paid on behalf of President Donald Trump ahead of the 2016 election.

Vanity Fair and The Wall Street Journal independently cited anonymous sources on Friday morning (AEST) as saying David Pecker, CEO of American Media, had been assisting the investigation.

Mr Trump’s former lawyer Michael Cohen pleaded guilty to eight criminal counts in a federal court on Tuesday, including tax fraud, false statements to a bank and campaign finance violations, as part of a plea deal with federal prosecutors.

“I and the CEO of a media company, at the request of the candidate, worked together” to suppress stories, he told the court in New York.

Court papers connected to the guilty plea said American Media CEO Mr Pecker offered to help Mr Trump squash negative stories during the 2016 campaign.

The WSJ said Mr Pecker shared details with prosecutors about payments  Cohen alleged Mr Trump directed him to make in return for the silence of two women claiming to have had affairs with him.

The hush money was paid to adult film actor Stormy Daniels and former Playboy model Karen McDougal.

Australian-born Dylan Howard, American Media’s chief content officer, is also reportedly cooperating with investigators.

Court documents filed by federal prosecutors cited “encrypted” communications between Mr Pecker, Mr Howard and Cohen regarding the payoff to Ms Daniels.

Mr Howard negotiated the purchase of rights to Ms McDougal’s story for US$150,000 ($210,000) and Mr Cohen subsequently sought to buy those rights, the NYT reported.

Mr Pecker has maintained a friendship with Mr Trump for decades.

In the late 1990s, as chief executive of Hachette Filipacchi Magazines, he published the quarterly Trump Style, distributed to guests at Trump properties.

He has also been a frequent guest at Mr Trump’s Mar-a-Lago resort in Palm Beach.

US media has reported that the Cohen’s testiony could pressure Democrats to launch impeachment hearings should they win a congressional majority in the November mid-term elections.

“This is a very big deal,” Neal Katyal, a US solicitor general in the Obama administration and now a white-collar criminal lawyer, was quoted as saying by The Washington Post on Thursday.

“The President of the United States has been directly implicated in federal crimes, and implicated not by some enemy but by his own personal lawyer,” Mr Katyal said.

-with agencies