Based on Chapter 606 ( If you didn't read it yet, What are you waiting for? Go Now!) Madara said in order to get the Rinnigan, you must be an Uchina with the Sharingan and have Senja's DNA.
So since all the doujutsu are connected and the Hyuuga are somewhat related to the Uchina. If Neji, Hinata, or anyone else has Uchina's DNA, They will have the Sharingan!?
So since all the doujutsu are connected and the Hyuuga are somewhat related to the Uchina. If Neji, Hinata, or anyone else has Uchina's DNA, They will have the Sharingan!?