Nagato Uzumaki got the Rinnegan from Madara, he never awaken it himself as Nagato was unable to awaken it. Madara also stated that the Rinnegan was the last form of the Sharingan, so you would need the Sharingan to awaken the Rinnegan and I can't see Naruto getting the Sharingan. Currently there have only been 2 people who have awaken the Rinnegan, those are Madara and the Sage himself.
Madara awaken the Rinnegan close to his death and implanted his eyes in Nagato, giving Nagato the Rinnegan. Obito later took Nagato's Rinnegan's and implanted one of them into himself. So not a single Uzumaki or Senju have ever awaken the Rinnegan, only had it because they were given to them through implants.
Sharingan Development
Sharingan 1 Tome -> Sharingan 2 Tomes -> Sharingan 3 Tomes -> Mangekyou Sharingan -> Enternal Mangekyou Sharingan -> Rinnegan