Washington (CNN) The FBI is in possession of a recording between President Donald Trump and his former personal attorney Michael Cohen in which the two men prior to the election discuss a payment to a former Playboy model who has alleged an affair with Trump, Rudy Giuliani and a source familiar with the matter told CNN Friday.

Cohen has other recordings of the President in his records that were seized by the FBI, said both a source with knowledge of Cohen's tapes and Giuliani, who described the other recordings as mundane discussions. Another source with knowledge of the tape, however, said the conversation is not as Giuliani described and is not good for the President, though the source would not elaborate.

The recording about the former Playboy model, Karen McDougal, was among the troves of documents and materials seized in the FBI raid of Cohen's hotel, residence and office earlier this year amid a criminal investigation of Cohen by the US attorney's office for the Southern District of New York. A transcript of the recording was reviewed by the Trump legal team, which does not believe it poses a legal problem for the President.

The President has waived privilege on the McDougal recording, said two sources briefed on legal discussions surrounding the materials seized in April.

The recording had been deemed privileged by a former federal judge, known as a special master, one of the sources said, adding that Trump's lawyers have sent a letter to the special master asking to withdraw the privilege. This gives the government access to the recording as part of the US attorney for the Southern District of New York investigation into Cohen.

The September 2016 recording is the only recording of any significance involving the President, another source said, despite there being hundreds of recordings.

The disclosure of the McDougal recording, which was first reported by The New York Times, raises fresh questions about the lengths to which Trump and his confidant would go to suppress allegations of extramarital affairs from becoming public before the election. Adult film actress Stormy Daniels has sued Trump over a $130,000 agreement Cohen made to her on Trump's behalf to keep her quiet about an alleged affair, which Trump has denied, along with McDougal's allegations.

McDougal eventually signed a contract with American Media Inc., the company that owns the National Enquirer, which barred her from publicly speaking about the alleged affair before the 2016 election.

On the recording, Cohen and Trump discuss buying the rights to that contract from AMI, according to Giuliani, who described the contract as a "nondisclosure agreement." The discussion, Giuliani said, involved their intention "to reimburse AMI for what they laid out and to do it by check, properly recorded."

The conversation was relatively quick, between approximately 90 seconds and two minutes, a source familiar with the tape said.

Giuliani added that "nothing in that conversation suggests it was a campaign contribution. There's no discussion about harm to the campaign" during the recorded conversation, which took place two months before the presidential election. The discussed payment to AMI ultimately never happened, according to Giuliani.

The source familiar with the tape said Cohen recommends buying the rights to the story and Trump asks questions about how they would go about doing that.

A source familiar with the AMI deal with McDougal disputed Giuliani's description of the deal. The source said it was not a nondisclosure agreement but a license agreement that clearly outlined the nature of its editorial aspects of the agreement.

Campaign-finance law experts say that if a payment is made for the purposes of influencing an election -- for example, to quiet allegations that could harm a candidate -- it can be considered a campaign contribution even if it isn't made from a campaign account. If such payments were made routinely and would have occurred regardless of the existence of any campaign, however, they may not be regarded as in service of an electoral effort.

Trump lashes out; other attorneys react

Giuliani said Trump had no idea he was being recorded during the McDougal discussion, which took place in the then-candidate's office at Trump Tower in September 2016. When informed about the recording, Trump said, "I can't believe Michael would do this to me," a source familiar with the tapes told CNN.

Trump lashed out at Cohen on Twitter Saturday morning, saying it was "inconceivable that a lawyer would tape a client - totally unheard of (and) perhaps illegal."

Inconceivable that the government would break into a lawyer's office (early in the morning) - almost unheard of. Even more inconceivable that a lawyer would tape a client - totally unheard of & perhaps illegal. The good news is that your favorite President did nothing wrong! — Donald J. Trump (@realDonaldTrump) July 21, 2018

A spokeswoman for the US attorney's office and Cohen declined to comment. Cohen's attorney, Lanny Davis, told CNN in a statement the recording will not hurt Cohen.

"Obviously, there is an ongoing investigation and we are sensitive to that," Davis said. "But, suffice it so say, that when the recording that has been widely reported is heard, it will not hurt Mr. Cohen. And any attempt to spin cannot change what is on the tape."

After Trump's tweet, Davis added Saturday in a post on Twitter: "The strategy of @realdonaldtrump @potus @RudyGiuliani is flawed; just as is #Trump's false #Twitter statement made against @michaelcohen212 this morning. Rudy claims the tape is "exculpatory". Why so angry?"

When asked about Davis' tweet, Giuliani told CNN: "How would you feel if your lawyer was recording you without telling you. The tweet is straightforward and correct."

McDougal's attorney Peter Stris tweeted on Friday: ".@karenmcdougal98→ When @realDonaldTrump said we were lying, do you think he meant we WEREN'T?" an apparent reference to Trump's claim of having misspoke at the summit with Russian President Vladimir Putin earlier this week.

When asked by CNN if first lady Melania Trump had a comment on the news of the recorded conversation, her spokeswoman Stephanie Grisham said in a statement, "Mrs. Trump remains focused on her role as a mother and as First Lady of the United States. We will have no further comment on the topic."

Part of the criminal investigation of Cohen by the US attorney's office has examined possible election law violations related to payments made to women who alleged sexual encounters with Trump. One focus of the searches in April, CNN has reported, was to seek records on Cohen's payments to Daniels, who has alleged such an encounter, and on an agreement set up between McDougal and AMI, whose chairman and CEO is a close friend of Trump.

Cohen hasn't been charged with any wrongdoing.

Other recordings exist

JUST WATCHED NYT reporter: Clearly Trump knew about payment Replay More Videos ... MUST WATCH NYT reporter: Clearly Trump knew about payment 01:49

There are other tapes of Cohen and other "powerful" individuals that the FBI seized beyond the President that could be embarrassing for the people on the tape and for Cohen, according to a source familiar with the tapes. The source said the people are of "significance and consequence."

The source familiar with the Cohen tapes said there was nothing illegal about the discussion, but acknowledged there could be ethical issues about Cohen recording his own client.

Giuilani has known about the tapes for several days, and has reviewed the transcripts, he told CNN.

In recent weeks, documents and other evidence obtained during April's searches has begun to be turned over to the government as the special master, Cohen's lawyers and lawyers representing Trump and the Trump Organization have moved through the process of determining which of the millions of items are subject to attorney-client privilege. The special master, Barbara Jones, however, so far has found the vast majority of the items reviewed to be not privileged, according to court filings, indicating that very little of what Cohen did in recent years qualified as legal work.

In recent weeks, Cohen's public remarks have raised suspicions that he could be willing to seek a cooperation agreement with the US attorney's office that would require him to provide information federal prosecutors could use against other individuals they are examining. It's not clear, however, whether the US attorney's office would be willing to grant Cohen such an deal.

In an interview with ABC News that was released earlier this month , Cohen said that protecting his family -- as opposed to Trump -- is his priority.

"My wife, my daughter and my son have my first loyalty and always will," Cohen said.

McDougal free to discuss allegations

JUST WATCHED Karen McDougal and the 'catch and kill' system Replay More Videos ... MUST WATCH Karen McDougal and the 'catch and kill' system 02:53

In August 2016, McDougal signed an agreement with AMI, Us Weekly, Men's Journal and several other publications. She believed at the time the contract was a work agreement that would allow her to be photographed for and write pieces that would run in the companies' publications.

Her attorney for that negotiation was Keith Davidson. She told CNN she later found out Davidson was in contact with Cohen. In a lawsuit, she accused Davidson of "working closely with representatives for Mr. Trump while pretending to advocate on her behalf." Davidson denied the allegations and told CNN that he reached out to Cohen during the final stretch of the 2016 campaign as a "professional courtesy" to let him know that he negotiated the deal with AMI.

McDougal later realized she could face a financial penalty for speaking to the media about her story. In April, she reached a settlement with AMI that allows her to discuss the alleged affair.

Speaking with CNN's Anderson Cooper in March, McDougal alleged that she and Trump were together "many dozens of times" and answered in the affirmative when asked if they were intimate.

McDougal described the alleged affair from 2006 to 2007 as a consensual, loving relationship, and said she did not know Trump might have seen other women at the time besides his wife -- and that throughout their relationship, he did not use protection.

On Friday, asked if the President still denied McDougal's allegations of an affair, Giuliani said: "I haven't asked him again. I don't know if that's changed, but none of this tape suggests that he did."