The group cites a 2007 University of California Irvine study of Californian prisons, which found that trans women were 13 times more likely than the general population to be sexually assaulted in men's prisons.
Rimutaka Prison director Chris Burns told Newstalk ZB this morning that the Corrections facility only received the request at the weekend and it was being treated with urgency.
In a letter to No Pride in Prisons, Follett said she had problems with some Corrections officers when she was on remand, but most had treated her alright - apart from some misgendering.
"A couple of inmates had caused some s**t, but she shut them down pretty quick," Ms Shields said.
Follett was sentenced to 21 months in jail on July 4 on a charge of injuring with intent, after she stabbed a man in his 40s she met on a dating website when she was 19.
After Follett cut off contact with the man, who has name suppression, he continued to try to reach her in a series of text messages that culminated in a threatening text on May 26.
When he turned up at her home, Follett met him in the driveway armed with a knife and stabbed him four times.
At the time of sentencing, she had already spent six months in custody, most of that segregated or in isolation.
The Department of Corrections allows anyone to apply for a transfer if they identify with a different gender.
If their application fails, they are accommodated to the sex recorded on their birth certificate.
Follett's lawyer Elizabeth Hall has yet to respond to requests for comment.
No Pride in Prison's hunger strike will begin tomorrow outside St Kevin's Arcade on
Auckland's Karangahape Road, if Follett is not moved before then.
- Additional reporting: Newstalk ZB
