Trump was referring to Cohen's ownership of taxi medallions, which are being examined by FBI investigators.
Cohen's camp has denied being the source of the CNN report, the basic substance of which The Associated Press independently confirmed.
"The man is a liar", Giuliani says. But he has said since no "meaningful information" was offered and that the meeting focused mostly on adoptions of Russian children.
But after the release of the Trump-Cohen recording, Trump criticized his former attorney, saying on Wednesday, "What kind of a lawyer would tape a client?"
Cohen is under a federal investigation probing allegations of bank fraud, wire fraud and violations of campaign finance law, and prosecutors are said to have seized many covert recordings in an April raid on his Manhattan office and hotel room.
Giuliani - the public face of Trump's legal team - has offered up wildly divergent characterizations of the president's longtime attorney and fixer in the months since the Federal Bureau of Investigation raided him in April.
In regard to reports that a so-called "joint defense agreement" between Trump and Cohen has been severed, Giuliani told Fox News he does not know if the agreement has been formally renounced.
Three days after Cohen's new lawyer, Lanny Davis, released a tape of Cohen and Trump talking about paying for Playboy model Karen McDougal's silence, the relationship splintered further Friday.
Seth Wenig AP FILEMichael Cohen arrives to court in New York
Trump denied knowledge of the meeting once again in a blistering tweet directed at Cohen.
Cohen is "trying to make a deal, no doubt about it", Giuliani also said.
Cohen, who once declared fierce loyalty to the president, is under federal investigation in NY for his business dealings and reportedly whether hush payments violated campaign finance laws.
Trump and his legal team claim the president knew nothing of the meeting until after it had taken place and until The New York Times approached him about the meeting in June 2017.
Trump Jr. testified previous year to the Senate Judiciary Committee that his father had no knowledge of the meeting with the Russians. A statement from Donald Trump Jr. one day earlier made no mention of Clinton.
I suspect that a long line of presidents would dispute Trump's "tougher on Russia" claim, particularly Ronald Reagan. Trump Jr. responded that if the information was good, "I love it", and the two began to arrange the rendezvous. Trump Jr. says he didn't get any dirt at the meeting - and the promised speech never happened.
But according to Goldberg on Friday, Giuliani doesn't appear to be helping Trump with his uncontrolled response to the Cohen revelations, which include his flip-flopping on Cohen's credibility.
"The only Collusion with Russian Federation was with the Democrats, so now they are looking at my Tweets (along with 53 million other people) - the rigged Witch Hunt continues!"