If there is one man Hibari wants to fight even more than Reborn and full power!Tsuna, it is Rokudo Mukuro. During the Kokuyo Arc, Hibari suffers a humiliating defeat at the illusionist's hands and has since sought to repair the situation. Many times throughout the series, he is convinced to stand down from current battles in favor of a future one with Mukuro. He knows how powerful the man is but it still doesn't deter him from his search for a rematch. Mukuro himself appears to be waiting patiently for the battle as well, acknowledging in the Inheritance Ceremony Arc about just how powerful Hibari is becoming. In the Kokuyo Arc, when Mukuro possesses Hibari's heavily injured body, he is surprised that the prefect was even able to move with his body as broken as it was. Mukuro seems to have a lot of respect for Hibari's strength following that incident.