I can't find a primary source but several random web pages recite this same story:
> "I'll never forget the day Marilyn and I were walking around New York City, just having a stroll on a nice day. She loved New York because no one bothered her there like they did in Hollywood, she could put on her plain-jane clothes and no one would notice her. She loved that.
> So as we we're walking down Broadway, she turns to me and says 'Do you want to see me become her?'
> I didn't know what she meant but I just said 'Yes'- and then I saw it.
> I don't know how to explain what she did because it was so very subtle, but she turned something on within herself that was almost like magic. And suddenly cars were slowing and people were turning their heads and stopping to stare. They were recognizing that this was Marilyn Monroe as if she pulled off a mask or something, even though a second ago nobody noticed her.
> I had never seen anything like it before."
> ~ Amy Greene, wife of Marilyn's personal photographer Milton Greene
See https://www.sunnyskyz.com/blog/2610/No-One-Recognized-Marily...
I presume it's from a biography or published interview, but I can't find it.[1] Google, and especially Google Books, is a ghost of its former self and only gets worse with time.
There's a slightly different retelling from a book review:
> "Do you want me to be her?" Marilyn said to the friend. "Watch." And taking off the headscarf and opening her coat to thrust out her chest, she went into the MM sashay, and within half a minute was surrounded by a baying mob of fans and autograph hunters.
See https://www.theguardian.com/books/2012/aug/03/marilyn-monroe...
[1] I did find this promising citation,
> Mailer, interview with Amy Greene, in Mailer--UT; "Milton Greene," B & W: Black and White Magazine, Spring 1949
visible when searching for "Greene" in the Google Books preview of Marilyn: The Passion and the Paradox. The year seems suspect, though, as Amy Greene (nee Amy Franco) didn't marry Milton Greene until 1953. (EDIT: I think the first part of that citation is to Norman Mailer's 1973 biography, Marilyn: A Biography, and the second part possibly to the photograph which Mailer was expositing. So perhaps his book is the original source of the Amy Greene quote. Though the literal veracity of his accounting is suspect, AFAICT. I don't think his book was a typical biography, but rather something of an artistic gloss on the concept of a biography.)