President Trump has denied having sex with Daniels.
Federal investigators are looking into Cohen's business dealings, including the $130,000 payment.
Former New York City Mayor Rudy Giuliani sent a warning to special counsel Robert Mueller on Wednesday: stay away from Ivanka Trump.
Daniels has since sued Trump and Cohen claiming that the non-disclosure agreement she signed was invalid. He hasn't said whether Trump personally reimbursed him. Cohen, meanwhile, has legal troubles of his own. "He represents me, like with this insane Stormy Daniels deal, he represented me", he said, again on Fox News.
'That money was not campaign money, sorry.
Giuliani continued: 'Everybody was nervous about this from the very beginning. "It's not campaign money".
Giuliani said the president knew the general arrangement but didn't know the specifics.
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Daniels" lawyer, Michael Avenatti, called the comment "a stunning revelation'.
"Mr. Trump evidently has participated in a felony and there must be serious consequences for his conduct and his lies and deception to the American people", he said.
Rick Hasen, an election law expert at the University of California, Irvine, noted that, despite Giuliani's claims, "Cohen would have still made an illegal loan to the campaign" if it is determined that the payment was related to the campaign.
"That was money that was paid by his lawyer, the way I would do, out of his law firm funds or whatever funds, it doesn't matter".
Ingraham played a clip of Trump on Air Force One from April 6, 2018 denying he knew about the $130,000 payment to Daniels, and denying knowing where Cohen got the money from. Giuliani provided the most definitive link yet between the president and Daniels, a $130,000 payment that the White House - and Cohen - have tried to distance from Trump.
Cohen has said he made the payment independently, without Trump's knowledge and without looping in the Trump Organization - a move that would be unusual and unethical, as lawyers don't generally make payments on behalf of clients without their knowledge. Giuliani said that Trump told Cohen, "We'll cover your expenses", and agreed to pay him $35,000 a month "out of his personal funds" over the course of a year-long period that began in the first few months of 2017 and has since ended.
"If this is true then it looks like Cohen may have made an unreported loan to the campaign rather than a contribution", said Richard L. Hasen, an expert in election law at the University of California, Irvine.