Well, Naruto might name the cat after one of his ninja moves, like Rasengan. And the cat could become his little sidekick, following him around the village. It could even learn some ninja - like behaviors from Naruto.
His life would become more domestic. He would have to worry about things like feeding the cat and cleaning its litter box. Also, he would have a constant companion at home, which would make his place feel more like a home rather than just a place to sleep.
He would be protective of the cat. Given his nature of always wanting to protect the weak, if any threats came towards the cat, Naruto would be the first to step in. He might also talk to the cat a lot, sharing his dreams and stories about his adventures, even if the cat couldn't understand his words.
One great fanfiction with this premise could be 'Midoriya's Feline Adventure'. In it, Midoriya's transformation into a cat brings out some really cute and funny situations. His friends initially don't recognize him, and there are a lot of misunderstandings that lead to comical scenes. For example, Bakugo tries to shoo him away thinking he's just a stray cat, not realizing it's Midoriya.
One common theme is transformation. The presence of the cat often changes Loki in some way, like making him more empathetic. For example, in many stories, Loki starts to care for the cat's well - being, which is new for him as he was more self - centered before.
In 'naruto as a cat fanfiction', Jiraiya could be an interesting character to interact with Naruto as a cat. He might see some potential in this cat - form Naruto for some new ninja techniques. The Akatsuki members could also interact with Naruto as a cat. For example, Itachi might sense something unusual about this cat when he passes through the village. And Konohamaru could be another character. He would be really excited to have a cool cat friend, not knowing it's Naruto.
Well, 'A Cat for Loki' is another great one. In this fanfiction, Loki finds a cat that can travel between different realms. He decides to keep the cat and they go on all sorts of adventures together. The author does a great job of describing the different realms they visit and how Loki's relationship with the cat evolves during their travels.
Perhaps it was a weapon created by a rogue ninja with unique powers. And for some reason, it found its way to Naruto in Wave. It might also be a weapon that was enchanted by a sorcerer long ago and has special abilities that Naruto will discover as he uses it.
One possible scenario in this fanfiction could be that Naruto's sister constantly interferes in his ninja training. She might think the training is too dangerous for him and tries to stop him from taking on challenging missions. For example, when Naruto is about to go on a mission to the Land of Waves, his sister could try to convince the Hokage not to send him, believing that he's not ready yet. This would add a whole new layer of conflict to the story, not just between Naruto and his sister, but also with the village's expectations of Naruto as a ninja.