Let's start with the requirements for awakening the Rinnegan. From the Naruto Wikia,
the Sharingan can be evolved into Rinnegan through combination with Hashirama's DNA.
In the history of the Naruto anime, the only 2 people who have been able to pull such a feat are Madara and Sasuke. What those 2 have in common is the Eternal Mangekyou Sharingan which they awakened from taking their brothers Mangekyous.
Obito on the other hand had a normal Mangekyou Sharingan and that explains why he was unable to evolve his sharingan to the Rinnegan despite having both bloodlines.
So my deduction is: the highest point of the Sharingan (aka the Eternal Mangekyou) plus Hashirama's cell/chakra (or Otsutsuki bloodline which can be gotten from mixing both Senju and Uchiha genes) = The Rinnegan.
Now to the question, in my opinion, if Naruto took Sasuke's Eternal Mangekyou Sharingan and implanted them into his eyes, then he would manifest the Rinnegan. This is because he would meet the requirement for the evolution, which are:
- Eternal Mangekyou sharingan
- Otsutsuki bloodline (or a mixture of both Senju and Uchiha chakra).
But then again let's be realistic, Naruto would never do that.