Katerina Sakellaropoulou, 63, has served as president of the Council of State, a top administrative court, for the past 15 months.
Two center-left opposition parties have already backed Sakellaropoulou's nomination, raising the total number of lawmakers from parties declaring support to 266.
Greece has a historically low level of women in senior positions in politics. In the current cabinet, all but one of the 18 senior positions are held by men. The president holds a largely ceremonial position and serves a five-year term. If elected, Sakellaropoulou will succeed President Prokopis Pavlopoulos, a 69-year-old veteran conservative politician and academic.