Unfortunately, the old man most likely did not know that the man living with him was going to start a plot to kill him. However, I do not believe the main character of The Tell-Tale Heart was a psychopath; he was more likely a sociopath, which is slightly different. (I have included a link that explains the difference between the two; please do not use it as an entirely reliable source for diagnosis, this is just a way to differentiate between the two for purely a literary interest.) The narrator mentions that he had previously held no ill will towards the old man, who had never insulted him, or injured him.
That is one of the tragic aspects of this story: this was not something that the narrator initially meant to do; he only wanted to kill the old man because he did not like the look of the old man's eye, which was something the old man had no control over. In essence, the old man had no way of knowing his fate, and no way of preventing it.