Minister for Social Protection Joan Burton has told her Cabinet colleagues that ex-gratia compensation may be appropriate in the case of Lydia Foy.
Ms Foy fought a 12-year court battle to have the Government recognise her gender.
Ms Foy, who underwent sex reassignment surgery in 1992, lost a High Court challenge to have her gender recognised on her birth certificate.
However, she subsequently succeeded when the case came back before the court in 2007.
The Government subsequently abandoned efforts to appeal the ruling and agreed to progress the legal recognition of transsexuals.