Donald Trump's longtime lawyer, Michael Cohen, secretly taped a discussion with him about payments to a former Playboy model who says she had an affair with the US president, and the tape is now in FBI hands, The New York Times reported Friday.

The FBI seized the recording earlier this year during a raid on Mr Cohen's office, the newspaper said in a bombshell revelation, quoting lawyers and others familiar with the recording.

Mr Cohen, who no longer represents the president, is being investigated over payments made to women to hush up embarrassing news stories about Mr Trump ahead of the 2016 presidential election.

FBI agents seized computers, phones and documents in an April raid on the lawyer's home and office as part of an ongoing investigation into his business dealings, including any information on payments made in 2016 to former Playboy model Karen McDougal.