For a 'naruto training crossover fanfic', you could do a crossover with the Bleach universe. Naruto could train with Ichigo. Ichigo's ability to transform and his sword skills could inspire Naruto to develop new jutsu. Also, Naruto's stamina and willpower could be an example for Ichigo. Another option is to cross Naruto with characters from Hunter x Hunter. The nen abilities in Hunter x Hunter are complex. Naruto could learn about nen and use some concepts to enhance his chakra usage. And the Hunters could learn about ninja stealth and combat from Naruto. Maybe Naruto could also train with Killua, and they could have a friendly sparring match to exchange skills.
One idea could be to have Naruto train with characters from other popular shonen series like Goku from Dragon Ball. They could exchange training techniques, for example, Naruto teaching Goku about chakra control while Goku shows Naruto how to better use his physical strength. Another idea is to have Naruto cross over with characters from Fairy Tail. The Fairy Tail mages could introduce Naruto to different types of magic-based training that he could incorporate into his ninja training. A third idea would be to have Naruto train with characters from One Piece. They could have a unique training session on a deserted island, learning survival skills from each other.
Well, in a 'naruto training crossover fanfic', a really cool crossover would be with the Avatar: The Last Airbender world. Naruto could train with Aang. Aang could teach Naruto about bending the elements, and Naruto could show Aang some of his ninja techniques. They could both learn about different ways of using their powers. Also, Naruto could cross over with the characters from My Hero Academia. The students at U.A. High could introduce Naruto to modern hero training methods, and Naruto could teach them about the importance of self - discipline and hard work in training, which are key aspects of his own training journey.