In her 2014 book The Fame Lunches, Merkin revealed she became friends with Allen after writing a letter to him.
She credited the director with supporting her while she struggled with depression, revealing he also encouraged her as a writer.
Merkin said she spent time in person with Allen and they continue to stay in touch on and off.
A New York Magazine spokesman told Page Six that Merkin's relationship with Allen is "disclosed and part of the story".
"Soon-Yi Previn is telling her story for the first time, and we hope people will withhold judgement until they have read the feature," the statement reads.
"Daphne Merkin's relationship to Woody Allen is disclosed and is a part of the story, as is Soon-Yi's reason for speaking out now."
Representatives for Dylan said she was not interviewed for the story and that the magazine only reached out to her for fact checking after it was already written.
The piece is only expected to include a short quote from Dylan.
Dylan's allegations against Allen, which first came to light in 1992, have resurfaced in the #MeToo era.
Farrow's accusations made headlines again when she called out actresses who showed public support for the Time's Up initiative but still worked with Allen.
"I fully support women taking a stand, linking arms with other women (and men), advocating on behalf of one another to effect change not only in the entertainment industry but in the world at large," Farrow said in a statement.
"That is an admirable and worthwhile objective, I hope these women change the world.
"That said, the people who join this movement without taking any kind of personal accountability for the ways in which their own words and decisions have helped to perpetuate the culture they are fighting against, that's hard for me to reconcile."
Celebrities including Colin Firth, Mira Sorvino, Timothée Chalamet, and Michael Caine have since said they regretted working with Allen in the past.
Allen later claimed he was the "poster boy" for the movement, portraying himself as a victim and saying it was unfair he was linked with Harvey Weinstein.
"What bothers me is that I get linked in with them," he said. "People who have been accused by 20 women, 50 women, 100 women of abuse and abuse and abuse."
"And I, who was only accused by one woman in a child custody case which was looked at and proven to be untrue, I get lumped in with these people."
Allen said he was "distressed" that Dylan's accusations were damaging his career amid the #MeToo movement.
"I think in any situation where anyone is accused of something unjustly, this is a sad thing," he said.
"This is something that has been thoroughly looked at 25 years ago by all the authorities and everybody came to the conclusion that it was untrue.
"And that was the end and I've gone on with my life. For it to come back now, it's a terrible thing to accuse a person of.
"I'm a man with a family and my own children. So of course it's upsetting."
Dylan's allegations first came to light during a bitter custody battle in 1992.
Allen, who went on to marry Previn in 1997, was investigated over the rape claims but was never charged. He has repeatedly denied the allegations.
Farrow won custody of the couple's three children, and Allen was stripped of visitation rights with Dylan.
In her 2014 open letter published in the New York Times, which opened Allen to a new round of scrutiny, Dylan, now aged 32, described in detail the alleged rape in the attic.
"He told me to lay on my stomach and play with my brother's electric train set," she recalled.
"Then he sexually assaulted me. He talked to me while he did it, whispering that I was a good girl, that this was our secret, promising that we'd go to Paris and I'd be a star in his movies.
"I remember staring at that toy train, focusing on it as it traveled in its circle around the attic. To this day, I find it difficult to look at toy trains."
