In May, Giuliani said that Cohen was "honest", and just a few weeks ago he said he didn't think Cohen would lie, saying, "I think he is going to tell the truth". "If they rely on him ... it would destroy whatever case they have".
Asked about former Trump campaign chairman Paul Manafort's upcoming trial, Giuliani told CNN "New Day" co-anchor Alisyn Camerota that Manafort "was not involved with intimate business relationships with Donald Trump".
But both CNN and NBC reported - citing anonymous sources - that Mr Cohen is willing to assert his claim to Special Counsel Robert Mueller, who is investigating Russian interference in the 2016 presidential election and possible collusion with Mr Trump's campaign.
President-elect Trump greets Rudy Giuliani at Trump National Golf Club in New Jersey in November 2016.
Giuliani said that if Cohen is aiming for a pardon by threatening to testify about the June 2016 meeting, "this is a stupid way to do it". And he has said in the past that the president didn't know about this nothing.
Giuliani's comments echo similar statements made by other members of the Trump camp, including the president himself.
Trump Jr. famously replied: "I$3 f it's what you say I love it". The tape, which was released last week by Cohen's attorney, was one of a dozen audio recordings seized by Federal Bureau of Investigation agents during an April raid on Cohen's home, office and hotel room, CNN reported.
Following the report on the Trump Tower meeting, Giuliani told CNN's Chris Cuomo on Thursday that Cohen has "been lying for years ... he's lied all his life", and said he doesn't "see how he has any credibility". One of the several topics he discussed with host Alisyn Camerota was Special Counsel Robert Mueller's Russian Federation probe, and how long he thinks it will continue.
Cohen's lawyer, Lanny Davis, however, referred to Giuliani as "confused", adding that the President "expressly waived attorney client privilege last week and repeatedly and inaccurately - as proven by the tape - talked and talked about the recording, forfeiting all confidentiality".
Giuliani told Fox he has hired technicians to determine if someone tampered with the tape, which cuts off abruptly. Trump Jr. says he didn't get any dirt at the meeting - and the promised speech never happened.
In an ABC News interview released on July 2, Cohen said his family and the country commanded his "first loyalty", the first fuel to that speculation.