Tiffany Scott, who stalked a 13-year-old girl while known as Andrew Burns, reportedly requested a transfer to a women’s prison.
The Daily Record newspaper reported this request has been rubber-stamped after previously being refused.
Any transfer would likely not be to HMP Cornton Vale as it is expected to be replaced by a new facility called HMP Stirling later this year.
Earlier this week, Isla Bryson was initially taken to Cornton Vale after being convicted of two rapes which took place when she was a man known as Adam Graham.
Bryson was later transferred to a prison on the male estate, understood to be HMP Edinburgh.
It is understood no transfer is imminent in Scott’s case.
Scottish Conservative equalities spokeswoman, Rachael Hamilton, said Scott has also attacked female staff while in a men’s prison.
She said: “The fact that such a violent and dangerous criminal is set to be transferred to a women’s prison is absolutely appalling.
“It is clear that Tiffany Scott continues to present a grave risk to the safety of any women that come in contact with them – even trained prison staff.”
She continued: “Nicola Sturgeon has repeatedly tried to reassure the Scottish public that the Scottish Prison Service’s risk assessment would protect women from predatory men, yet the process is clearly not fit for purpose if this dangerous offender has been approved for transfer to a women’s jail.
“Women’s safety must not take a backseat to the wishes of violent criminals.
“Nicola Sturgeon has already U-turned under public pressure to belatedly remove double rapist Isla Bryson from a women’s jail, she must now intervene to block the transfer of this violent individual before it takes place, or knowingly risk the safety of some of Scotland’s most vulnerable women.”
A Scottish Prison Service (SPS) spokesman said: “We do not comment on individuals.
“Decisions by the SPS as to the most appropriate location to accommodate transgender people are made on an individualised basis, informed by a multi-disciplinary assessment of both risk and need.
“Such decisions seek to protect both the wellbeing and rights of the individual as well as the welfare and rights of others around them, including staff, in order to achieve an outcome that balances risks and promotes the safety of all.
“Where there are any concerns about any risks posed by an individual, either to themselves or others, we retain the ability to keep them separate from the mainstream population until an agreed management plan is in place.”
A Scottish Government spokeswoman said: “The placement of prisoners is an operational matter for the Scottish Prison Service who use comprehensive individualised risk assessments to inform decisions, such as the appropriate location of transgender people in custody.
“SPS is reviewing their policy on managing transgender prisoners in partnership with the Scottish Government and that process is nearing completion.”