The recording was seized when the Federal Bureau of Investigation raided Cohen's home and office in April.
Friday's reports raised questions about why Trump's campaign denied knowledge of the deal between McDougal and American Media when it became public, and they fanned speculation about how much damage Cohen might be able to inflict on the president.
A person familiar with a federal investigation into Cohen tells The Associated Press that Cohen made the recording two months before Trump's 2016 election. "And any attempt to spin can not change what is on the tape". They claim that Giuliani is mischaracterizing the tape in key ways that contradict the facts of the conversation as they see them. "Second, the tape, as well as a lawyer's notes, are privileged and non-public".
AMI, American Media Inc., is the parent company of the National Enquirer. "They're talking about a corporation doing it, one of their corporations doing it. The President says 'make sure it's done correctly, and make sure its done by check'".
The President's lawyer also sought to position the President as wronged by the recording. Citing a source familiar with the tapes, CNN reported that Trump, when informed about the September 2016 tape, said, "I can't believe Michael would do this to me". He said the payment discussed was never actually made, and Mr Trump had done nothing wrong.
The president has responded to the allegations, calling them "inconceivable" and saying that a lawyer taping a client is "totally unheard of & perhaps illegal". Rudy claims the tape is "exculpatory". "The tweet is straightforward and correct". Assuming that the conversation didn't take place when Trump was in one of the twelve states with all-party consent laws (the location of each party matters), then the recording is legal and usable by prosecutors in court.
Trump raises questions over seized Cohen recording
"So not only is suggesting that Cohen committed a crime in recording him, but to accuse his former lawyer, who simply said may have the goods on him of committing the crime is a awful, bad idea", Specter continued.
On the recording, Cohen and Trump discuss buying the rights to that contract from AMI, according to Giuliani, who described the contract as a "nondisclosure agreement".
Trump had previously defended Cohen after he came under pressure by investigators linked to the Russian Federation investigation, but rumors have swirled that Trump's personal lawyer might not be so loyal. "Very foolish strategy by team Trump".
"Nothing in that conversation suggests that he had any knowledge of it in advance", Giuliani said.
The FBI investigation stemmed in part from a referral by the US special counsel's office, which is looking into possible coordination during the election campaign between Trump's aides and Russian officials.
Despite the President's comment Saturday, he has waived privilege on the recording, said two sources briefed on legal discussions surrounding the materials seized in April.
A self-described fixer for Trump for more than a decade, Cohen said a year ago he would "take a bullet" for Trump.