Trump had initially said publicly that he believed his longtime fixer would remain loyal to him, but Cohen has increasingly suggested he's preparing to cooperate with the feds as he grows more and more isolated from his former boss.
"Inconceivable that the government would break into a lawyer's office (early in the morning) - nearly unheard of", Trump tweeted, in an apparent reference to an Federal Bureau of Investigation raid on the office of his former lawyer Michael Cohen in April. "Even more inconceivable that a lawyer would tape a client - totally unheard of & perhaps illegal". "The good news is that your favorite President did nothing wrong!".
The Post also reports that the "The recording, which Cohen made surreptitiously in Trump Tower in early September 2016, was seized by federal agents who are investigating Cohen for potential bank and election-law crimes, according to multiple people familiar with the probe".
Trump's attorney Rudy Giuliani confirmed to The Times that Trump discussed payments to McDougal with Cohen, but he said that ultimately no payment was made.
The former model, Karen McDougal, said she began an almost yearlong affair with Mr Trump in 2006 shortly after his wife, Melania, gave birth to their son, Barron, the Times said.
He suggested Cohen's motivation could be that, "if he still entertains the thought that the president might pardon him, the putting of this tape in the public domain is a pressure point on the president that he can do the president great damage".
Giuliani said the discussion of payment did not mean McDougal's claim of an affair was true and characterized it as an attempt to resolve false allegations that were "personally damaging" to Trump.
The former Playboy model said that after their first sexual encounter, Trump tried to offer her money.
Mitchell Epner, an attorney at Rottenberg Lipman Rich who was previously an assistant USA attorney for the District of New Jersey, told Business Insider that Cohen could have made the recording either "for his own protection" or to ensure he got repaid for an expenditure he thought could have been agreed to in the conversation.
Giuliani also denied Trump had an affair with McDougal.
While, such tapes do not necessarily imply guilt on the part of Cohen or the President, Trump's reaction certainly doesn't sound like something coming from an individual with nothing to worry about.
The White House has said that Mr Trump denies having an affair with Ms McDougal and that he has denied having sex with Stormy Daniels.
Non-disclosure agreements of the type signed by Ms Daniels and allegedly by Ms McDougal are not in themselves illegal.
FILE PHOTO: U.S. President Donald Trump's personal lawyer Michael Cohen arrives at his hotel in New York City, U.S., May 11, 2018.
Giuliani said the proposed payment was a personal matter and not subject to campaign finance law.