Madara was able to get the Rinnegan by mixing Hashirama's meat with his own (i.e. mixing the Indra and Asura chakras) to get the Sage's power. If Naruto did the same by mixing Sasuke's meat with his own, would he get the Rinnegan? Or, if Sasuke mixed Naruto's meat with his own, would he get Rinnegan in both of his eyes?
Naruto could obtain the Rinnegan by means of transplanting. The only option would be taking the eyes from uchiha madara whom already awaken the Rinnegan. On the other hand he could not awaken a Rinnegan by just mixing uchiha cell to his body. The best option would be like what Danzo did, with his uzumaki chakra he might able to handle the sharingan's chakra drainage issue. For sasuke part he may awaken the Rinnegan using the same technique Madara used. But all this is a speculation answer, by means in theory sake based on the whole manga series. Only Kishi Sensei could tell otherwise.
I'm sure there's two ways for one to achieve the Rinnegan. One, obviously through the means of transplantation from someone who doesn't want a Rinnegan (which is freaking NOBODY), or the Indra Ashura reincarnation process. For an Indra reincarnate to achieve Rinnegan, they must have Sharingan, take chakra from the reincarnation of the current Ashura reincarnate; thus reforming Hagoromo's chakra, and a Rinnegan awakens. If Naruto, who possesses no Visual Jutsu, took Sasuke's chakra, I'd assume he'd achieve Rikudou Senjutsu? But maybe, just MAYBE, if he took a Sharingan, then Sasuke's chakra, he just MAYBE could awaken a Rinnegan. Not completely certain.