Their relationship could start with mutual understanding. Naruto, who has always had a connection to the Kyuubi, now with a female form, could start to see her as more than just the beast inside him. They could have conversations about his dreams and her past.
Another way is through shared experiences. For example, they could fight side by side against a common enemy. In the heat of battle, they rely on each other, which makes their bond stronger. This could then lead to feelings of love and affection developing over time. In a more detailed sense, after the battle, they might take care of each other's wounds and have a moment of vulnerability that brings them closer. As they continue to have more shared experiences like this, their relationship blossoms.
Their relationship could also grow through mutual respect. The female Kyuubi respects Naruto's strength and determination, and Naruto respects her power and the fact that she has been trapped for so long. This respect can lead to a friendship or even something more as they rely on each other more and more in difficult situations.
The relationship can be developed through shared battles. When they fight side by side against foes, they can start to trust each other more. For instance, if they face a powerful enemy that neither could defeat alone, they would rely on each other's strengths.
One way is through shared experiences. If they are both put in a situation where they are in danger, like being trapped in a genjutsu together. They have to work together to break free. This would force them to communicate and rely on each other. Also, the male Kyuubi could start to see Naruto's dreams of peace and be influenced by them. He might then start to support Naruto more actively in his pursuits.
There could also be a romantic relationship in some fanfics. This would bring a whole new dynamic to the Naruto universe. It might start with small moments of mutual understanding and attraction, gradually evolving into a full - fledged love story. However, this would also face many challenges, like the differences in their nature (human vs. tailed beast) and the opinions of others in the ninja world.
The relationship can be developed through mutual respect. Naruto could respect the Fem Kyuubi's power and knowledge, and in return, she could respect his determination. For instance, they could start off as wary of each other but gradually learn to trust. They might share stories about their pasts, with Naruto talking about his lonely childhood and the Fem Kyuubi about her long existence. This sharing could create a connection between them.
At first, Naruto might be a bit scared or hesitant. But as the female Kyuubi shows her care and concern for him, he would start to trust her. They would gradually develop a mother - son type of relationship. The female Kyuubi could be strict at times to make Naruto a better shinobi, but also very loving.
In fanfiction, Tsunami might have a special ability that can soothe the Kyuubi's wild nature. Naruto, being the host of the Kyuubi, is amazed by this. They start to work together, with Tsunami using her ability regularly on the Kyuubi. This leads to a more harmonious relationship between Naruto and the Kyuubi, and also a deep friendship between Tsunami and both Naruto and the Kyuubi as they rely on each other more and more.
The jealousy can act as a catalyst for their relationship. For example, when the female Kyuubi is jealous, Naruto might start to notice her more. He'll be curious about why she's acting that way, and this newfound attention can lead to them spending more time together. As they interact more, they could start to understand each other better and develop deeper feelings.
A very unique way would be if they get trapped in a time - loop together. They have to rely on each other to break free and in the process, they learn things about each other that they never knew before, leading to a deep and different kind of relationship.
Their relationship can start with mutual respect. Naruto, in his godlike form, respects the power of the Fem Kyuubi. The Fem Kyuubi, in turn, respects Naruto's newfound divinity. This respect can gradually turn into friendship as they fight side by side.