Their relationship could become more of a peer - to - peer one. Since Naruto already has a lot of knowledge and skills from his future self, he might be able to offer new perspectives to Jiraiya. Jiraiya could see Naruto in a new light and start to rely on him more in certain situations.
In the past, Jiraiya might become more protective of Naruto. Knowing what Naruto will become in the future, he may be extra cautious about any threats that come their way. At the same time, Naruto could look up to Jiraiya even more as he witnesses Jiraiya's younger self in action and realizes how much he has learned from him.