My theory as to why Naruto will gain the Rinnegan.
1) The SO6P was the jinchuuriki of the Juubi and had both light and dark chakra. According to plot, Naruto is slowly being acknowledged as the reincarnated version of the SO6P by the Bijuu themselves, the ones who dealt with the Sage directly. Their combined fist bump and name recognition already hints at their acceptance of Naruto as the "one who will lead them down the right path" or basically the jinchuuriki of their combined chakra which we all know as the Juubi.
2) If this is true Naruto cannot fully become the SO6P unless he acquires shadow side of chakra since he already has the light side (life/physical energy).
3) This being the case the Juubi was composed of ten tails and a single eye that resembled a Sharingan eye with nine tomoe. In my opinion the tenth tail was a physical manifestation of that sharingan-like eye. If one looks at the back of the cloak worn by the SO6p there are nine tomoe and a Rinnegan at the top. The Rinnegan is the tenth tail.
4) By becoming the Juubi's jinchuuriki I believe he will acquire the shadow chakra that seems to be embodied in the Rinnegan.
I know that this theory is incomplete but I feel that is has some merit and plausibility.
Makes sense. Seems pretty like the metaphore of the
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where the light represents knowledge (The Bijuu's consciousness that aknowledges the love inside Naruto and give him their trust) and darkness that represents the blind status quo (the power itself that Sasuke had currently until now, known as Sharingan).
The Knowledge shall guide the blind beast. That's alike what the SO6P said to the tailed beast, someone would "guide them" on the right path.
In the other way, Itachi told Sasuke about "whatever Sasuke decided", he would trust and love him. The Cycle of Hatred is the story that was being repeated through the Uchiha bloodline, in the quest for power they would sacrifice their friends so they could awaken a more powerful level of their eyes. This cycle is the Status Quo itself, and the trust Itachi gave to Sasuke (as well as the deceased Hokages answers) gave him the key to break the cycle.
That told, it's pretty possible that both Naruto and Sasuke becomes new SO6P. Sasuke doesn't need the Juubi, because he already was in the path of Darkness in the quest for power. What he needs now is to break the cycle of hatred, and he will find the answer inside his within. In the other way, Naruto walked the path of light, but he still needs to walk the path of Darkness... so there is the Juubi, the Dark part Naruto lacks currently.
Conclusion: Naruto can become a SO6P if he becomes the Ten Tails Jinchuuriki. Sasuke can become a SO6P if he overcomes hatred and embraces darkness to find the light, that is, knowledge.
