The user can also use this Haki to predict an opponent’s moves shortly before they make them, thereby making the attack much easier to evade with enough skill. This prediction appears to the user as an image or brief “premonition” of what the opponent will do in the user’s mind’s eye.
After last chapter, we discovered that Katakuri has trained his observation haki so much that he can see a bit into the future.
However considereing the plethora of strong characters we’ve already seen so far, it’s safe to assume that Oda already showed us more of this power. 
1/. Gold Roger:
Throught the story, it has been stated multiple times that Roger and his crew were waiting for a certain person to continue their mission.
Shanks even went as far as to give his arm and his captain’s straw hat to Luffy because he believed he was the one.
At this point it seems as if Roger planned his death and informed his crew about the person he was waiting for, knowing that that that person would need his help.
Couldn’t then Roger, who was arguably the strongest character shown in One Piece have seen more than a few moments in the future? 
2/. Momonosuke:
Contrarily to Roger, Momonosuke isn’t someone who could have trained his Haki enough to surpass the likes of Katakuri.
However, as shown with his ability to control Zunisha, he is clearly born with great spiritual power.
It is to note that Momonosuke wasn’t the first character able to use Haki without training. In Skypeia, the little girl Aisa was shown to be able to use Mantra (observation Haki) since birth.
So what does this have to do with observation Haki? Back in Zou, the crew and the Minks talk about Roger and Momonosuke mentions that he’s met him before. Everyone brushed this off as a lie in the moment for fun.
Could’ve Momonosuke had a vision of meeting Roger? That doesn’t seem very likely at first, as observation Haki enables its user to look into the future and not the past.
However after further thinking, like Oden with Roger, Momonosuke could very well accompany Luffy to Rafter and somehow meet a version of the pirate king there.
3/. Madam Shyarly:
Madam Shyarly is a mermaid, who’s also a fortune teller. At the age of four she made a prediction about the coming of the Great Age of Pirates and many pirates indeed came to the island one year later.
At some point, she listened to Hatchan’s story about Silvers Ryleigh. Before the Whitebeard War, Shyarly predicted Whitebeard’s death and he indeed met his end.
Like Aisa and Momonosuke, Shyarly could also be one of those innate Haki users.
4/. Honorable mentions:
– The Great Kingdom: The Great Kingdom was said to be an extremely powerul kingdom. Not only were they in control of the three ancient weapons, but they also had the power to sentence a creature like Zunisha to walk for eternity.
It would be safe to assume that they had powers far exeeding those of the current One Piece world.
Could they then have predicted their own inevitable downfall and create the poneglyphs for that reason?
– Monkey D. Dragon: It is said that Dragon was always a step ahead of the world Government.
Is that due to his observation haki? Did he predict Luffy being in danger both in Logetown and in Saboandy? Did he foresee Blackbeard attacking Baltigo?
*Theory by District
