AI inner monologue

In many a science fiction future there's an intelligent computer that dialogues with the human characters, providing them advice and challenge. Would it be possible to have this input as an inner monologue? You inner monologue would become a dialogue between you and your AI assistant. How would such a thing work? I haven't a clue, we'd need an incredibly good understanding of the brain to start inputting to the inner monologue.

But the impact would be enormous. The AI assistant could help with memory ("your car keys are under the sofa cushion"), moral decisions, finding out information, highlighting where you have fallen for logical fallacies, etc.