The move has been welcomed by the LGBT community, but has exposed political divisions, and church opposition.
Currently, Greece requires people who wish to have their desired gender legally recognised to be diagnosed with "gender identity disorder", and have their reproductive organs removed.
This practice has been condemned as a violation of human rights, though is common in many European countries.
The bill has been tabled by the ruling leftist Syriza party and will be put to a vote tomorrow.
It says that changing legal gender is a matter of personal choice, and should not be contingent on medical tests, therapies and surgeries.
The draft legislation says person have the right to change legal gender twice, and applicants must not be married. A court will decide on their application.
But an article setting the minimum age for the change to 15 years has bared cracks in Prime Minister Alexis Tsipras' coalition.
His ally, the right-wing independent Greeks, said it would vote against the bill, unless the age was amended to 17 years.
It's been condemned as "immoral" by Greece's influential Orthodox Church.
