Many One Piece fans believe that if the right-hand man of the Pirate King, Rayleigh can have Conqueror’s Haki, then the right-hand man of the future Pirate King, Zoro can certainly possess it.
The parallel between Zoro and Rayleigh is pretty high. Scar on an eye, scar on chest, both heavy drinkers, both loners before joining Luffy/Roger, both swordsmen.
The essential traits of those who have Conqueror’s Haki are ‘strong willed, wild, wilful, unconstrained and unrestrained‘. Zoro easily fits this description. Also, there were several instances which hinted that Zoro could have Conqueror’s Haki.
During the Fishman Island Arc, when Luffy knocked out 50,000 foes with Conqueror’s Haki, Zoro said that if he didn’t possess it, it would be time for Luffy to step down from being captain. Hence, many people believe that Zoro also possesses it.
One of the key features of Conqueror’s Haki is intimidation. In Punk Hazard Arc, Zoro was able to intimidate Monet to such an extent she was unable to move.
The intimidating aura that Zoro has been hinted here and there (most recently when the Sumo in Wano fled and left Okiku because Zoro had a mysterious aura) and his 9-sword style that he exhibited versus Kaku and the Pacifica could be a manifestation of advanced Conqueror’s Haki, similar to how “the breath of all things” he exhibited at Alabasta is, as we learned in Chapter 939, a form of advanced Armament Haki.
All of these moments kinda hints that Zoro probably has/will have Conqueror’s Haki.
Zoro has a tremendous strong-will to become the strongest swordsman. If we equate ‘strongest swordsman = King of swordsmen’, this boosts the chance of him having Conqueror’s Haki.