CBS News has learned that shortly before the 2016 election, attorney Michael Cohen secretly recorded a conversation he had with his client, Donald Trump. They discussed making a payment to a Playboy model, Karen McDougal, who claimed she once had an affair with the future president, CBS News Washington correspondent Paula Reid reports.

The phone call was made just two months before the presidential election. Federal investigators uncovered the recording, which runs about two minutes, in April during raids on Cohen's home and offices.

The Justice Department is investigating Cohen's role in paying women to stay silent about their claims of affairs with Mr. Trump in the run-up to the 2016 election. If the payments were made to help get him elected, they may be violations of federal campaign finance laws.

Get Breaking News Delivered to Your Inbox

McDougal says she began a nearly year-long affair with Mr. Trump in 2006. Just a few months before the election, the publisher of the National Enquirer purchased her story but never published it.

"He always told me he loved me," McDougal told CNN earlier this year. She told Anderson Cooper that she believed National Enquirer's purchasing of the story was a favor for Mr. Trump in the last few months of the presidential election.

The White House on Friday did not respond to CBS' inquiries, but has repeatedly denied the affair, issuing a statement in February saying "this is an old story that is just more fake news. The president says he never had a relationship with McDougal."

Cohen's attorney Lanny Davis said in a statement "when the recording is heard, it will not hurt Mr. Cohen. Any attempt at spin can not change what is on the tape."

The president's attorney, Rudy Giuliani, told The New York Times the recording also would not hurt his client. The New York Times first reported the existence of the tape of Cohen and Mr. Trump.

Payments to women have become a topic the White House and Mr. Trump's lawyers have had to address in recent months. In May, Giuliani revealed on Fox News that Mr. Trump repaid Cohen for a $130,000 payment Cohen made to adult film star Stormy Daniels ahead of the election in 2016. Daniels, like McDougal, claims to have had an affair with Mr. Trump. Giuliani insisted that there was no campaign finance violation in that instance.