Sasuke could also train Naruto in this fanfiction. They have a rivalry - turned - friendship. Sasuke has his own unique skills and knowledge, especially with his Sharingan and the fire - style jutsus. Training with Sasuke would be intense and would likely result in Naruto developing skills that are more in line with Sasuke's combat style, while also bringing out new aspects of their relationship.
Another option could be Itachi. Although Itachi is from a different village and has his own complex situation, in a fanfiction scenario, he could secretly train Naruto. Itachi has extremely powerful jutsus and a deep understanding of the Sharingan. Training under him would give Naruto a very different perspective on power and combat, not to mention some insights into the Uchiha clan.
Well, in such a fanfiction, Naruto might be trained by someone else entirely. Maybe he gets trained by Jiraiya right from the start more intensively. This could lead to Naruto having a different fighting style, perhaps more focused on toad - related jutsus earlier on.
Maybe Kakashi could be the one. He's always been Naruto's mentor in many ways. He has the knowledge and skills to train Naruto for such an unusual task. He could use his Sharingan to analyze the fanfiction and teach Naruto how to spot the dangerous elements within it.
Well, it could be that in this fanfic, Kakashi discovers a new potential in Naruto. He might train Naruto in some ancient and forgotten ninja arts. This would set Naruto apart from his canon self. Also, their relationship could be explored more deeply, like Kakashi becoming a father - figure to Naruto, and this emotional bond could influence Naruto's growth as a ninja.
Another reason could be that in this fanfiction, the plot is set in a way that there is a new training system in the village. And this system doesn't involve Kakashi in Naruto's training. There could be new mentors or a completely different approach to training young ninjas like Naruto, which excludes Kakashi from the equation.
Well, Kakashi could train Naruto in combat skills specific to ANBU missions. This would include more lethal and precise attacks. He might also teach Naruto how to use different types of weapons that are common in ANBU operations. Maybe Kakashi would set up mock battles where Naruto has to face multiple opponents at once, just like in real ANBU scenarios.
Well, Kurama might train Naruto by teaching him how to better control and access chakra. Since Kurama has a vast amount of chakra, it could show Naruto unique ways to harness and use it. For example, it could guide Naruto in creating more powerful and complex jutsu by using their combined chakra in a more efficient way.
One possible reason could be that Kakashi might be haunted by his past experiences. He has lost many comrades, and perhaps he's afraid that getting too close to Naruto and training him would put Naruto in danger as well. He might think that Naruto, being the Jinchuriki of the Nine - Tails, already has a target on his back, and training him would only make that target bigger.
Naruto might be initially very disappointed. He has always looked up to Kakashi as a strong and cool ninja, and being refused by him would be a big blow. He could become a bit sulky and withdrawn, feeling like he's not good enough.
In such a fanfiction, Naruto might become extremely powerful under Kakashi's training. He could learn new jutsus faster and gain better control over his chakra. Maybe he'd also develop a closer bond with Kakashi, different from his relationship with Iruka or other characters in the original story.
Sasuke could be a side character. Since Naruto is getting special training from Kakashi, Sasuke might feel jealous or motivated to train harder himself. Sakura could also be there, perhaps she tries to learn from Kakashi's training methods to help Naruto better. Another potential side character could be Iruka, who might check on Naruto's progress from time to time and offer some words of encouragement.