Michael Avenatti said he received a call late Sunday from two prosecutors who said they were concerned about media interest in the interview and canceled the meeting, according to the Associated Press.
Daniels and Avenatti have been cooperating with prosecutors and provided documents about the payment, made shortly before the 2016 election, in response to a subpoena, said the person, who spoke on the condition of anonymity to provide the information about Monday’s interview.
A spokesman for the U.S. attorney and attorneys for Cohen declined to comment.
Cohen is under federal investigation for possible campaign finance violations as well as bank and wire fraud. An FBI raid of his New York law office and home included a search for records related to the Daniels payment.
Cohen has acknowledged making the payment through one of his Delaware business entities.
The payment came in the final weeks of Trump’s campaign, and the president has recently said he was aware that Cohen made an arrangement with Daniels, an adult-film star whose real name is Stephanie Clifford.
White House officials have repeatedly denied that Trump had a sexual relationship with Daniels.
Daniels is suing Trump and Cohen in California to invalidate the confidentiality agreement she signed at the time of the payment. A federal judge in April granted Cohen’s request for a delay, saying it appeared likely that Cohen would be indicted in the criminal investigation in New York.
Daniels is also suing the president for defamation in New York federal court; a response to her claim is due by July 23.
Cohen is also under scrutiny by special counsel Robert S. Mueller III in the investigation into Russian interference in the 2016 election.
Devlin Barrett contributed to this report.