CNN cited anonymous sources saying Mr. Cohen was willing to share his information with Mr. Mueller, who is investigating possible collusion between Trump's campaign and Russian Federation.
At first, Trump Jr. said he never told his father of the meeting then later told Senate investigators that he couldn't recall who he spoke with that night.
Weisselberg's name came up earlier this week on an audio recording that captured then-nominee Donald Trump talking with his former attorney Michael Cohen about a payment to acquire the rights to the story of a former Playboy model who had claimed she and Trump had an affair, which the Trump campaign later denied.
A former Trump Organization employee told CNN that Weisselberg being subpoenaed as part of the Cohen probe is the "ultimate nightmare scenario for Trump" because Weisselberg knows "anything and everything" about the finances of the Trump Organization. In response, a source close to Cohen mocked Giuliani, saying, "You mean Rudy is floating reckless, fact-free, false, wild speculation as if he were unhinged?"
Cohen recently turned to prominent attorney and lobbyist Lanny Davis, a long-time associate of Bill and Hillary Clinton, to represent him. "Sounds to me like someone is trying to make up stories in order to get himself out of an unrelated jam", the President tweeted.
"The president was very disappointed in Michael Cohen as he's tweeted particularly because he was a friend but also because he was a lawyer and acting as a lawyer during that conversation", Giuliaini said. More Dem candidates say they won't back Pelosi McCarthy on choosing the next Speaker: "I want it to be me" Judge rejects Trump attempt to dismiss emoluments clause lawsuit MORE told him of the offer from the Russians and that Trump approved going ahead with the meeting.
Giuliani was even more explicit in his praise of Cohen in May, saying that Cohen is "an honest, honorable lawyer" when ABC's George Stephanopoulos asked if he was concerned that Cohen, who is under criminal investigation by the USA attorney's office in Manhattan, would cooperate with prosecutors.
"I did NOT know of the meeting with my son, Don jr".
The Thursday reports of Cohen's claims is further evidence that Cohen could flip on Trump in the Russian Federation investigation - which would be a nightmare for Trump's legal team.
On Sunday, Giuliani told CBS that talks since have been interrupted by other issues, including the Cohen matter and Mueller's prosecution of former Trump campaign manager Paul Manafort. If Mr. Cohen, who specialised in making deals and making Mr. Trump's problems go away, were to cut a deal, he would do so with an eye toward eliminating or cutting his potential punishment.
Still, Nunberg noted that Trump would have known about the Russian Federation lawyer meeting "under normal circumstances".
The (FBI agent Peter) Strzok report shows a guy off the wall who ran the original investigation hates Trump and claims he's not biased but he hates him. Mr Trump has denied the affair. The Russian government said through intermediaries to Trump Jr. that it was supporting Trump and wanted to help the campaign. They also note that two days before the meeting, Trump mysteriously announced plans to give a "major speech" about Clinton's scandals.
Sources tell CNN numerous tapes include discussions with reporters and conversations relating to President Trump.
"Robert Mueller and his gang of 13 Angry Democrats obviously can not find Collusion", Trump said during a new set of tweets, so "now they are looking at my Tweets (along with 53 million other people)".