In One Piece Vol. 98, author Eiichiro Oda revealed that even though he doesn't have a Devil Fruit currently, if Zoro were to have one, it would be the Uo Uo no Mi. The current holder of the Uo Uo no Mi? None other than Kaido, who, as of this writing, is busy inciting war alongside Big Mom against the Straw Hats in the manga's Wano Arc -- a war Zoro is front and center in. What was Oda trying to say by revealing this secret, if anything? How are Zoro and Kaido alike so much that they both could use the Uo Uo no Mi?
Oda could have meant that they are similar personality-wise. Zoro rarely engages in the same goofy antics of his crewmates and shows little interest in frivolous interactions, including romances. He would rather focus on his training and working towards becoming the world's greatest swordsman. He puts all of his focus on the task at hand and rarely strays away from whatever that is. He also recognizes the strengths of others, and when in battle, he is reckless to the point that he will continue to fight even if he knows his opponent is stronger.
Despite this, he makes sure that others who aren't involved will not get hurt because of him. He is prideful about his skills and ability to fight. In fact, it also seems the only thing he loves almost as much as his swords is alcohol.
This is something Kaido also enjoys. While he is normally arrogant and ruthless, he turns into a sobbing mess when he starts drinking. When he's drunk, he can do a total personality change, going from melancholic to hopeful in a matter of seconds. He also shares Zoro's belief in honor, as he views dying in battle as the most glorious way for a person to go out. He is also equally as reckless as the Straw Hat samurai when it comes to his own life, as he wants to wants to surpass his own inability to die. But, again, much like Zoro, he knows when an unnecessary fight should be avoided, particularly if he recognizes when someone is more powerful than they initially seem. Despite being villainous, Kaido also prefers fair, honorable fights to those where trickery is involved. Though that isn't to say he can't be treacherous.
While Kaido has the physique befitting someone who can transform into a giant dragon, Zoro is lacking in this department. It's likely he would have a lot of trouble controlling and mastering Kaido's Devil Fruit powers as a result. However, Oda's interview mentions another interesting tidbit: if Zoro were to possess the Uo Uo no Mi, he would combine it with one of his swords instead of ingesting it himself.
There have been past instances of inanimate objects being "fed" Devil Fruit, so having Zoro feed a sword actually makes sense when one considers that he wants to be known for his trained skills rather than anything else. He would rather stake his reputation on owning an Object Zoan and working with it as partners while still being a powerful swordsman in his own right -- rather than being someone who gained his skills and power from eating a piece of fruit.
So, while he and Kaido share many personality traits, it seems that he wouldn't want to end up being an unstoppable, unkillable monster that becomes bored with life, like Kaido.