"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.
The source said the clear suggestion by Avenatti to Cohen was to work together against Trump. An attorney for Cohen, Brent Blakely, said neither he nor his client "provided any information to Mr. Avenatti, are in any way cooperating with Mr. Avenatti, or have any interest whatsoever in cooperating with Mr. Avenatti to the detriment of President Donald Trump".
McDougal said she had a 10-month "romantic relationship" with Trump.
The New York Times reported that there was a surreptitiously-recorded dialogue between Trump and his longtime attorney Cohen where the two discussed a payoff to a Playboy "Playmate" with whom the then Trump had an affair. Cohen has not been charged with any crime.
The reports raise questions about why Trump's campaign denied knowledge of the deal between McDougal and American Media when it became public, and they have fanned speculation about how much damage Cohen might be able to inflict on the president.
New York, where the taping reportedly took place, legally requires only one person's consent for such a recording, suggesting it would not be illegal.
"I know for a fact that this is not the only tape". McDougal sold her story as an exclusive to the National Enquirer in August, 2016 for $150,000, though the tabloid never published her story - effectively buying her silence.
Prosecutors are apparently interested in payments he made on Trump's behalf to porn actress Stormy Daniels, and other business dealings related to Trump.
Lawyer Rudy Giuliani said no campaign funding was involved in the discussion between Trump and Cohen, who has distanced himself from Trump in recent months as the FBI investigates Cohen's business dealings.
Cohen, Trump's former personal attorney, is under investigation over his alleged practice of paying women to stay silent about claims they had sexual relations with the married Trump.
Under US election law, presidential candidates must disclose campaign contributions, which are defined as things of value given to a campaign in order to influence an election.
Trump has repeatedly lashed out at the seizure of Cohen's documents. In February, a White House spokesperson told ABC News, "This is an old story that is just more fake news".
Lawyers for Cohen could not immediately be reached for comment.