Conversion therapy refers to any form of treatment proposed to change a person's sexual orientation or to suppress a person's gender identity.
Minister O’Gorman has told his department to explore ways of banning the practice.
It comes as an all-island coalition to outlaw conversion therapy was formed this week.
Minister O’Gorman said the government “must be proactive in banning practices that not only propagandise harmful and discriminatory messages, but ones that also have serious negative consequences on a young person’s mental health, with the potential to inflict long-lasting damage.
“Legislating for a ban on conversion therapy will send a clear and unambiguous message to everyone, both younger and older, that a person’s sexual orientation, gender identity or gender expression is not up for debate," he said in a statement.
Sinn Féin Senator Fintan Warfield’s Prohibition of Conversion Therapies Bill of 2018 would prohibit conversion therapy as “a deceptive and harmful act or practice against a person’s sexual orientation, gender identity and, or gender expression.”
Almost 20 senators co-signed the bill when it was first put forward but almost three years later the bill has only reached the third stage in the Seanad.
The United Nations has urged the UK government to ban the practice during a debate last week.
The UN Special Rapporteur on Freedom of Religion or Belief, Dr Ahmed Shaheed, said that attempts to change someone's sexuality or gender identity were "haunting" and "chilling".
Addressing MPs on Thursday, Dr Shaheed said a ban would not violate freedom of religion or belief under international law, because of the harm involved in conversion therapy.
He told MPs: "International human rights law is clear that the right to freedom of religion or belief does not limit the state’s obligation to protect the life, dignity, health and equality of LGBT+ persons."
He went on to explain: "The testimonies of survivors of conversion practices are chilling. Operating on the basis that there is something “wrong”, “sinful” or “pathological” in non-heterosexual-cis forms of sexual and gender identity, LGBT+ persons are assailed with physical and emotional abuse that have haunting consequences.”