The 18-year-old Olympiacos playmaker is set to undergo a medical examination at Brighton before the proposed £34 million transfer is finalized.
Despite interest from Premier League giants Manchester United and Arsenal, both clubs decided not to make an official offer for Kostoulas.
During his breakout season in Greece, Kostoulas scored seven goals and provided one assist in 35 games across all competitions.
Brighton is investing heavily in Kostoulas, with the £34 million transfer fee being one of the highest in the club's history.
