According to the Journal, Trump, 71, and Clifford, 38, met at a celebrity golf tournament in July of 2006.
Cohen, the White House and Clifford have all denied that a steamy affair ever took place.
Around the same time as the reported payout, Trump's presidential campaign was hit with allegations that he had sexually harassed women, including a recording that Trump apologized for.
So, to sum up, Donald Trump allegedly had an affair in 2006 with a porn actress when his third wife was pregnant with his son and he paid her to keep quiet five days before he was elected President. The couple Wednesday in 2005.
The $130,000 payment part, however, is new.
In a statement to the Journal, Cohen did not address his role in negotiating the supposed payment but said Trump denies any such relationship with Clifford.
Cohen also accused the Journal of perpetuating 'a false narrative for over a year'.
The story was never published.
Evans told the website Trump knew "exactly" who Clifford was and "wanted to meet her", with the pair posing for a photo together which was later posted to her Myspace page.
"These are old, recycled reports, which were published and strongly denied prior to the election", said a White House official. In the draft, Clifford was referred to as Peggy Peterson and was represented by a lawyer named Keith Davidson, while the other parties were referred to as David Dennison and David Delucia.
However, he said, "Attorney-client privilege prohibits me from commenting on my clients" legal matters'.
It is the latest controversy to hit the under-fire president this week. He left after close to a decade after the election.
Cohen now serves as the president's personal attorney.
The next day, Daniels allegedly told Evans she ended up in a hotel room with Trump, and that he chased her around "in his tighty-whities". At the time, Mr Trump was under intense scrutiny for a series of sexual assault allegations and claims of sexism.
The attorney for Clifford was not quick to respond to the question but lawyer sent a full copy to BuzzFeed of Clifford's statement denying the affair dated January 10. However, Trump has managed to sidestep any allegation and continue with his presidential aspirations.
For her part, she has said Trump was a ideal gentleman.
Also in 2016, another adult film star said the Trump kissed her against her will at the same 2006 golf event.