Mr Trump and Michael Cohen discuss buying the rights to former Playboy model Karen McDougal's story. The lawyer then told Stephanopoulos that Cohen is not seeking a pardon from Trump - ending the interview by revealing his client has "more tapes" of the president.
This combination photo shows President Donald Trump and attorney Michael Cohen.
While Trump suggested over the weekend that Cohen may have acted illegally in secretly taping their discussion, jurists said it might not be so simple. When Cohen says, "Well, I have to pay -", Trump interrupts and says, "Pay with cash". "I think it's probably in his (Cohen's) interests to pursue some kind of deal".
Mr Giuliani said the president says "don't pay with cash".
Mr Trump is then heard saying "cheque". "After Michael Cohen mentioned financing". If skeletons are buried, it is assumed that Mr Cohen has the map.
"The tape contradicts Giuliani", Davis continued.
"There's no transaction done in green currency".
But if Cohen provides evidence of this, it could seriously damage Trump. If he winds up in investigators' crosshairs for secreting payoffs, he could potentially provide much more damaging information to prosecutors than Cohen ever could about the president's dealmaking. AMI bought the rights to her story of a relationship with Trump but instead of publishing it they sat on it.
"He never meant to make use of the recordings and certainly didn't intend to be deceptive", Davis said.
On Saturday, President Trump broke his silence over the recording, tweeting: "Inconceivable that the government would break into a lawyer's office (early in the morning) - nearly unheard of".
I don't know. His baseline point is certainly true, that attorney-client privilege wouldn't shield a conversation in which a lawyer and his client are conspiring to commit fraud. "The good news is that your favorite President did nothing wrong!"
The existence of the tape, secretly recorded by his former long-time attorney Michael Cohen two months before the 2016 election, was reported last week by the New York Times, which said the Federal Bureau of Investigation seized it during a raid on Mr Cohen's office this year, AFP reported.
Cohen can be heard in the tape telling Trump that he needs "to open up a company for the transfer of all of that info regarding our friend David", apparently referring to American Media Inc. head David Pecker. "In the big scheme of things, it's powerful exculpatory evidence", Giuliani added. He has since become the Trump Organization's chief financial officer and one of the president's closest business confidants (alongside Jason Greenblatt, who was Trump's in-house legal counsel before the president named him as a special diplomatic envoy to the Middle East).
If Trump made the alleged payments with his own funds, and made the payments strictly for personal, not campaign reasons, he could be legally in the clear.
Stories alleging that Trump paid off women or hid a pregnancy, or even a child, have always been brushed off by the president.
Shortly before the 2016 election, former Trump campaign spokeswoman Hope Hicks said that McDougal's allegations were "totally untrue".