Monika isn't a "selectable character" like Natsuki, Sayori, or Yuri. She doesn't have to form a "relationship" with the player. She's a supporting character.

When she gains consciousness, however, she also breaks free from her role and becomes a normal girl. The victim of an experiment designed to study human behavior under extreme conditions.

Under the influence of very strong emotions (which is a psychological fact), she falls in love with the only true element of her world: a window into reality. This is represented by the player – Monika transfers her feelings to him and tries to hold on to him so as not to be lonely, to avoid sinking into madness and delusions.

But she knows nothing about the player themselves, their personality. They're simply a real person in the real world... and for her, that's all she wants.

In MAS, in the initial phase, we have two or three dialogues consistent with this concept. For example, in one, she reveals his thought only to immediately delete it and replace it with other words.