"My father? Likely not," said Tymor. "My father is...very worldly and has been to most major places in the world. Though prone to exploration, I don't think he's spent enough time in King's Landing to discover those ways for himself."
He didn't doubt that his father might have theorized about their existence a long time ago...but it was only now that he might have genuine interest in the passageways for reasons other than exploration.
"Do you know of any passageways that lead to my family's quarters? I put a large, heavy chest of drawers in front of the one that leads to mine...it's not likely to prevent any night time intruders who are determined enough to get in, but at least it will prevent quiet entry."