Postecoglou has yet to secure a win in his first six games in charge, and Marinakis is looking for signs that the players are committed to the manager's approach.
The team's captain, Morgan Gibbs-White, has expressed his support for Postecoglou, and teammates have praised the high standard of training sessions under the Australian manager.
However, a win against Newcastle would be crucial in reassuring Marinakis and the board that the team is behind the manager and his methods.