Lanny Davis, a lawyer for Cohen, said he had no comment but told CNBC: "I have to wonder why the Trump people would put that out. It was not from us."
Word that Cohen is willing to cooperate with Trump's most significant current threat — the Mueller investigation — underscores the fact that the president and his former personal lawyer and longtime fixer are now in open warfare.
The stakes for both men are high: the legal fate of each hangs in the balance, and Trump's presidency potentially does as well.
Trump has repeatedly raged that the Mueller probe is a ''witch hunt'' and that there was ''no collusion'' with Russians by his campaign.
Last week, it was disclosed that Cohen had secretly recorded Trump when the two men were discussing a hush-money payment for a story involving Playboy model Karen McDougal in September 2016.
McDougal claims she had an affair with Trump beginning in 2006. Trump was already married at that time to Melania Trump, currently the first lady of the United States.
Audio of that tape includes Cohen mentioning to Trump that he and Trump Organization CFO Weisselberg had discussed setting up a company to make that payment.
The White House has denies Trump had sex with her, and Giuliani says no payment was ever made by Trump for her story.