Senior Republican staffers have likewise learned of the allegation and expressed concern about its impact on the nomination, The New Yorker added.
She admitted to being intoxicated during the alleged incident, and was at first tired of coming forward because of gaps in her memory.
Like Dr. Ford, Ramirez is calling on the FBI to investigate Kavanaugh.
Kavanaugh deinied the latest allegation.
Ford and Kavanaugh are set to testify before the Senate Judiciary Committee on Thursday to address the allegations after a week of fraught public negotiations between Ford's attorneys and Senate Republicans.
Trump, speaking in NY where he was attending the United Nations annual assembly, threw his full weight behind Kavanaugh whose once straightforward progress to the nation's highest court has been hit by two bombshell accusations of sexual misconduct from his school and university days. "But she can come and tell that story".
The New Yorker article was co-written by Ronan Farrow, whose reportage around disgraced movie mogul Harvey Weinstein was key in opening the floodgates of the #MeToo movement, along with another reporter Jane Mayer.
Earlier on Monday, the White House adviser Kellyanne Conway called the claims a "vast leftwing conspiracy" and said Kavanaugh should not have to pay for decades of "pent-up" demands by women for a cultural reckoning on sexual misconduct.
"I will not be intimidated into withdrawing from this process", Kavanaugh, a conservative federal appeals court judge nominated by Trump in July for a lifetime job on the top USA court, wrote in a letter to the Republican-led Senate Judiciary Committee, which is overseeing the confirmation process.
However, one former classmate remembered hearing about the incident from another, and independently corroborated numerous details offered by Ms Ramirez. Earlier in the day, the Senate Judiciary Committee announced that it will hear the testimony of Ford on September 27.
Kavanaugh states rather bluntly, "Last night, another false and uncorroborated accusation from 35 years ago was publishes". Ford has alleged Kavanaugh was "stumbling drunk" when it happened. The developments could also determine the fate of Kavanaugh's confirmation, which hangs on the votes of a handful of senators. "At a minimum, we need a hearing and investigations on all of the charges against him", said protester Sarah Newman, a 44-year-old Washington resident.
"I am with Judge Kavanaugh", Trump said in NY. "Lee looks forward to hearing from Dr. Ford and Judge Kavanaugh Thursday". "Not because they're supportive of President Trump's Supreme Court nominees, but because they have some standards".
A White House spokeswoman says the administration stands by the nominee, labelling the allegation "the latest in coordinated smear campaign by the Democrats created to tear a good man down".