However, Fox also reports that sources say Cohen has a "treasure trove" of information on the president.
During an interview on "Fox News Sunday", Giuliani called Cohen a "scoundrel" and a "liar".
Giuliani contended that Cohen is obviously out to hurt his former client.
The conversation was reportedly recorded in September 2016, two months before the 2016 presidential election. The government has been totally ethical about this, ' Giuliani said.
"Republicans and Democrats really should step back - it's tough to do - but let the investigation take its course", Costello said.More news: Roseanne Barr says she's feels forgiven for her tweet scandal
"I did NOT know of the meeting with my son, Don jr", Trump wrote in on Twitter after a CNN report cited his longtime lawyer Michael Cohen as saying Trump had known about the meeting in advance. Cohen has told people that Trump approved going ahead with the meeting with the Russians.
On the tape, Cohen and Trump discuss a payment to Karen McDougal, a former Playboy model who alleges she entered into an affair with Trump years before he became president.
'There are then an untold number of other tapes. However, it was Trump's legal team that actually waived protections that would have allowed the recordings to remain hidden from prosecutors, a source familiar with the matter told CNBC last week.
At a CNN town hall in April, former FBI Director James Comey, whom Trump fired, said collusion "is not actually a thing that exists under the federal laws of the United States".
Giuliani said the revelation of those tapes was "a very good development for us" and showed Trump did nothing wrong.
"Sounds to me like someone is trying to make up stories in order to get himself out of an unrelated jam", Mr. Trump said. "This nonsense needs to stop!" Giuliani appears to be hinting that the Trump campaign did play footsie with the Russians knowingly, especially in the way he frames the question to Camerota, but that it's not a crime to have done so. And that direct line between Russian interference and the president has never been proved before.
Guiliani would not discuss the conditions his team is requesting for Trump to participate in an interview, but hinted that the President's legal team was interested in limiting the discussion to events before the election.