Shimotsuki Ryuma was known as the Sword God of Wano and valiantly defended the country against outsiders:
Zoro appears to be a Shimotsuki himself,
from SBS Volume 96:
He bears quite the resemblance to Ryuma:
Both Zoro and Ryuma expressed the desire to become the World's Strongest Swordsman:
Both were blamed for crimes they did not commit. Zoro was blamed for a street murder and stealing Shusui:
Ryuma was blamed for summoning a dragon and called a murderer:
Ryuma is quite famous for slaying a Western Dragon:
Oda might be setting Zoro up as the second Ryuma. One Piece Magazine Volume 6 outright says: "It's been several hundreds of years since Ryuma's death. Perhaps a strong samurai who people can call the 'second Ryuma' has already been born.":
Given that Ryuma's most iconic legend is slaying a dragon over the capital, in order for Oda to credibly depict Zoro as the second Ryuma, Zoro would have to play a huge role in the defeat of the dragon tyrant terrorising the country. This is very synergistic with the One Piece Magazine Volume 5 mentioning that a new legend of slaying an Eastern Dragon will be born. Just as Ryuma had his own legend of slaying a Western Dragon:
So also might Zoro forge his own legend by slaying an Eastern Dragon and saving the country.
Conclusion
The conclusion from the above is inescapable; Zoro will not fight Kaido in any significant capacity.