Background of the Rinnegan
The Rinnegan has been a mysterious power in the Naruto series. It is the most powerful of the three great dōjutsu (eye techniques) and grants its user access to a variety of powerful techniques. The Rinnegan is said to be the most powerful of the three eye techniques and it can be used to perform a variety of techniques such as controlling the six paths of reincarnation, using space-time ninjutsu, summoning animals, controlling the nine tailed beasts and the ability to perform the ultimate ninjutsu technique, the Infinite Tsukuyomi.
The Rinnegan first appeared in the Naruto manga in the form of a man known as the Sage of Six Paths. The Sage was the founder of the ninja world and is said to be the ancestor of all ninja clans. He also created the nine tailed beasts and was the first person to wield the Rinnegan.
The Possibility of Naruto Having the Rinnegan
The possibility of Naruto having the Rinnegan has been a topic of discussion since the start of the series. The biggest hint came in the form of a reference to the Sage of Six Paths. In an early chapter of the manga, Naruto is revealed to possess the same chakra as the Sage of Six Paths. This has led many fans to speculate that Naruto may have the genetic potential to develop the Rinnegan.
The possibility of Naruto having the Rinnegan has been further explored in various video games, novels, and films. In the video game Naruto: Ultimate Ninja Storm Revolution, a special transformation of Naruto is revealed to have the Rinnegan in both his eyes. In the novel Naruto Shippuden: The Seventh Hokage and the Scarlet Spring, Naruto and Sasuke have a special transformation known as the Sage of Six Paths Mode which grants them access to the Rinnegan. In the film Boruto: Naruto the Movie, Naruto is revealed to have the Rinnegan in one of his eyes.
Why Naruto Might Not Have the Rinnegan
Despite the hints and evidence, there are still some factors that suggest Naruto might not possess the Rinnegan. The first is that the Sage of Six Paths was the only person to ever possess the Rinnegan and it is highly unlikely that Naruto could inherit the Rinnegan from him. The second factor is that Naruto is not a descendant of the Sage of Six Paths. Naruto is a descendant of the Uzumaki clan, which is unrelated to the Sage of Six Paths.
The third factor is that the Rinnegan is the most powerful dōjutsu and it is highly unlikely that Naruto could possess such a powerful technique. The fourth factor is that Naruto does not have the Six Paths of Reincarnation technique which is a prerequisite for the Rinnegan. The fifth factor is that the Nine Tailed Fox is not a part of Naruto's chakra, which is another prerequisite for the Rinnegan.
Conclusion
Despite the hints and speculation, it is still unclear whether Naruto has the Rinnegan or not. It is possible that Naruto may possess the Rinnegan in some form, but it is also possible that he does not possess the Rinnegan. It is something that only time will tell.
References
Naruto Wiki - Rinnegan
Naruto Wiki - Sage of Six Paths
Naruto Shippuden: The Seventh Hokage and the Scarlet Spring
Naruto: Ultimate Ninja Storm Revolution
Boruto: Naruto the Movie