She might want to pass on her knowledge and skills. Just like anyone else with expertise, she could see the value in teaching others what she has learned over the years.
Perhaps he's been influenced by someone who gives him bad advice. For example, if someone tells him that natural talent is enough and training is overrated. Also, he could be dealing with some personal problems, like a conflict within his family or among his friends that takes up all his time and mental energy, causing him to neglect training.
In this fanfiction, Hokage Naruto might take Naruto to a special training ground. There, he could teach Naruto some of his own unique jutsu combinations. For example, he could show Naruto how to combine the Rasengan with his Sage Mode more effectively. This would give Naruto a huge power boost and also make him more confident in battles against tougher opponents.
Motivation can be shown through a character's actions. For instance, if a character is motivated by revenge, they might constantly train to get stronger and seek out their enemy. Their dialogue can also reveal motivation. If they talk about their goals often, like protecting the village, it shows what drives them. Another way is through their reactions to events. A character motivated by friendship will go to great lengths to help their friends when they're in trouble.
One possible motivation could be power. Orochimaru is always seeking more power, and Naruto has the power of the Nine - Tails. He might think that by killing Naruto and somehow harnessing the Nine - Tails' power, he could become even stronger.
It could be due to the current situation in the village. There might be threats that required Naruto to stay. Tsunade, as the Hokage, had to consider the overall safety and stability of the village. So, she denied Naruto's request for the training trip to ensure he was available in case of any emergency.
Well, in the 3 - year training fanfiction, Naruto could also have some intense mental growth. He might learn more about the history of his clan and the ninja world from Jiraiya. This knowledge would not only make him a better ninja but also shape his understanding of his place in the world and his responsibilities.
Perhaps it's an old enemy who has a change of heart. This enemy could think that by training Naruto, they can make amends for their past wrongs. But Naruto, being cautious, denies the offer as he still has doubts about this former foe's true intentions.
In this fanfiction scenario, Naruto might learn unique chakra control techniques from Sarutobi. Sarutobi, being an experienced ninja, could teach Naruto how to better manage his large chakra reserves. This would lead to Naruto being able to perform jutsus more efficiently and with less waste of chakra.
Well, the result might be a fanfic that better adheres to the Naruto universe's rules and lore. For example, if the training focused on jutsu usage, the fanfic could then accurately describe how Naruto or other characters perform their jutsus. It could also result in a more immersive experience for the readers as the writing style gets polished during the training process.