Taiwan's pioneering gay rights campaigner, Chi Chia-wei, is one of the petitioners who has brought the case to the constitutional court.
After 30 years of activism, Chi, 59, told AFP he was "100 per cent confident" the ruling will go in his favour.
He urged the judges to allow gay couples to register to marry the next day if they approve a change in the law, rather than giving the government a longer timeframe to implement the decision.
At the heart of the case is a clause in Taiwan's Civil Code that an agreement to marry should be made between a man and a woman.