(CNN) Michael Cohen, President Donald Trump's former personal attorney, claims that then-candidate Trump knew in advance about the June 2016 meeting in Trump Tower in which Russians were expected to offer his campaign dirt on Hillary Clinton, sources with knowledge tell CNN. Cohen is willing to make that assertion to special counsel Robert Mueller, the sources said.

Cohen's claim would contradict repeated denials by Trump, Donald Trump Jr., their lawyers and other administration officials who have said that the President knew nothing about the Trump Tower meeting until he was approached about it by The New York Times in July 2017.

Cohen alleges that he was present, along with several others, when Trump was informed of the Russians' offer by Trump Jr. By Cohen's account, Trump approved going ahead with the meeting with the Russians, according to sources.

To be clear, these sources said Cohen does not have evidence, such as audio recordings, to corroborate his claim, but he is willing to attest to his account.

Cohen privately testified last year to two Congressional committees investigating Russian interference in the 2016 election. A source familiar with Cohen's House testimony said he did not testify that Trump had advance knowledge. Cohen's claims weren't mentioned in separate reports issued by Republicans and Democrats on the House Intelligence Committee.

Contacted by CNN, one of Cohen's attorneys, Lanny Davis, declined to comment.

Trump denied knowledge of the meeting in a tweet Friday morning.

"I did NOT know of the meeting with my son, Don jr. Sounds to me like someone is trying to make up stories in order to get himself out of an unrelated jam (Taxi cabs maybe?). He even retained Bill and Crooked Hillary's lawyer. Gee, I wonder if they helped him make the choice!" Trump tweeted.

An FBI raid on Cohen's office in April sought information about taxi owners who had financial dealings with Cohen, CNN has reported

Rudy Giuliani, the President's attorney, told CNN's Chris Cuomo on "Cuomo Prime Time" Thursday night that Cohen has "been lying all week, he's been lying for years."

"I don't see how he's got any credibility," Giuliani added.

Giuliani also said Cohen is "the kind of witness that can really destroy your whole case" and called Cohen, who was a top Trump Organization attorney for a decade, a "pathological liar."

"Donald Trump Jr. has been professional and responsible throughout the Mueller and Congressional investigations," said Alan Futerfas, an attorney for Donald Trump Jr. "We are very confident of the accuracy and reliability of the information that has been provided by Mr. Trump, Jr., and on his behalf."

According to people who have discussed the matter with Cohen, he has expressed hope that this claim about the Trump Tower meeting will help him reach out to Mueller and possibly lessen his legal troubles. He's under scrutiny by federal prosecutors in Manhattan after Mueller referred Cohen's case to them.

The June 2016 meeting was arranged after a publicist who knew Trump Jr. told him in emails -- in no uncertain terms -- that a senior Russian official "offered to provide the Trump campaign" with damaging information about Clinton, and that the outreach was "part of Russia and its government's support for Mr. Trump." At the time, the Russian operation to covertly boost Trump's candidacy wasn't publicly known. Trump. Jr. responded, "if it's what you say, I love it," and started to arrange the meeting.

At the meeting, Trump Jr. was joined by his brother-in-law Jared Kushner and Paul Manafort, who was Trump's campaign chairman at the time. There were four Russians in the room, including a lawyer with Kremlin ties, a businessman who worked for an oligarch and a lobbyist with old KGB connections.

After news of the meeting broke in July 2017, the Trump team offered misleading explanations and changed their story several times. But one claim stayed consistent: that Trump had no knowledge of the meeting beforehand, wasn't told about it afterward and first learned about it one year later.

Those denials were repeatedly issued by Trump, his attorney Jay Sekulow, Trump Jr., Futerfas and White House press secretary Sarah Sanders. Those people denied that Trump had contemporaneous knowledge of the meeting on more than 15 occasions, according to CNN's analysis.

Trump said on July 12, 2017, that he "only heard about it two or three days ago." One week later, Trump repeated that he "didn't know anything about the meeting" because "nobody told me" about it.

Around that same time, CNN's Jake Tapper asked Sekulow to confirm Trump's claims that he only recently learned about the controversial meeting. Sekulow's response: "Yes, I swear."

But perhaps the highest-stakes denial was given by Trump Jr. in his testimony last year to the Senate Judiciary Committee.

"He wasn't aware of it," Trump Jr. told lawmakers, referring to his father's knowledge of the meeting. "And, frankly, by the time anyone was aware of it, which was summer of this year, as I stated earlier, I wouldn't have wanted to get him involved in it because it had nothing to do with him."

Trump's critics have long doubted these denials. They point to a series of phone calls Trump Jr. made to a blocked phone number before and after the meeting. They also note that two days before the meeting, Trump mysteriously announced plans to give a "major speech" about Clinton's scandals. Trump Jr. says he didn't get any dirt at the meeting -- and the speech never happened.

Even Steve Bannon, the former White House chief strategist and top Trump campaign official, said the meeting was "treasonous" and speculated that "the chance that Don Jr. did not walk these (Russians) up to his father's office on the twenty-sixth floor is zero." Trump Jr. has denied Bannon's allegation. Bannon's comments, to author Michael Wolff for his book "Fire and Fury," triggered the bitter public divorce between Bannon and Trump in early 2018.

Axios reported that Bannon does not have first-hand knowledge about whether Trump Jr. told his father, and Bannon later said his "treasonous" remark was directed at Manafort and not Trump Jr.

UPDATE: This story has been updated with more comments from President Donald Trump and Rudy Giuliani.