Parliament has been debating the decades-old law that prohibits female students from covering their hair with an Islamic-styled scarf.
The key amendment that "no one can be deprived of their right to higher education" alludes to young women who wear headscarves.
The proposal is expected to pass the final round because of the number of seats held by the ruling Justice and Development (AK) Party, which sponsored the amendment, and the opposition MHP, which also backs the proposal.
The AK Party says the headscarf ban, imposed after a 1980 military coup, violates freedom of conscience and the right to education.
The move has angered secularists including the army, judiciary and academics who see the Islamic-styled headscarf as a symbol of defiance against the strict separation of state and religion, one of the founding principles of the Turkish republic.
They say lifting the ban would usher in a stricter form of Islam in the secular state and would, over time, lead to pressure on uncovered women to wear the Muslim garment.
Hakki Suha Okay, of the secular opposition Republican People's Party (CHP), said the party would challenge the reform in court if it is adopted.
He told the legislative assembly that the package "aims to render the principle of secularism ineffective".
"This step will encourage radical circles in Turkey, accelerate movement towards a state founded on religion, lead to further demands" against the spirit of the republic, he said.
The Democratic Society Party, the country's main Kurdish party which also opposes the proposal, said the move would only "lead to chaos and more problems rather than solve any".
Once the amendment is passed in Saturday's vote, it will be sent to Abdullah Gul, the Turkish president, for approval.
Turkey is 99 per cent Muslim. As recently as 1997, Turkey's army generals, acting with public support, ousted a government they deemed too Islamic.