Calling it "inconceivable" that a lawyer would record a client without their knowledge, Trump suggested the act was "perhaps illegal", but clarified that he "did nothing wrong!" in an early morning tweet.
The recording was seized when the Federal Bureau of Investigation raided Cohen's home, office and hotel room in April.
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.
CNN also reported that "a source familiar with the tape" said Trump responded to its existence by saying: "I can't believe Michael would do this to me".
His comments stoked speculation that Mr Cohen could co-operate with investigators against Mr Trump, but there has been no indication so far that he has done so. The FBI investigation is separate from special counsel Robert Mueller's probe of election interference in 2016 and potential obstruction of justice by those in the president's orbit.
Cohen's recording adds to questions about whether Trump tried to quash damaging stories before the election. Moscow denies US allegations that it interfered in the election and Trump denies any campaign ties to Russian officials.
In the lead-up to the 2016 presidential election, Ms McDougal sold her story to the National Enquirer, which is owned by a personal friend of Mr Trump, for $150,000 (£115,000).
Media captionWas Trump's Stormy Daniels payment legal?
The White House has said Trump denies having sex with Daniels.
A self-described fixer for Trump for more than a decade, Cohen said a year ago he would "take a bullet" for Trump.
The recording was first reported Friday by The New York Times.
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.
Federal prosecutors in NY are investigating Cohen for possible bank and tax fraud, and for possible campaign law violations linked to a $130,000 payment to Daniels and other matters related to Trump's campaign, a person familiar with the investigation has told Reuters.