Quick ponderance: We've seen the Rinnegan twice: Once from the great sage and once in Nagato.
Both were brought up in times of war and extreme personal stress. Kakashi suggests that the Rinnegan is some sort of randomly-occurring mutation. We've also seen that the sharingan appears in an Uchiha after experiencing stress.
Well what if the Rinnegan is a more extreme form of that? What if the Rinnegan appears in people who are experiencing EXTREME distress?
Madara said he wants to synchronize Sasuke with the Demonic Statue of the Outer Path. However, the only other person that we've seen work with that statue was Pain/Nagato.
Sasuke seems to be following a similar path guided by Madara. We've already seen in his battle with Danzou so far that his powers are increased by his hatred and his anger. There are plenty of things that are going to make Sasuke more angry:
1) Danzou's body is made of the disembodied parts of Sasuke's family and friends. We don't know whose sharingans Danzou stole, but I think when Danzou tells him whose eyes they are Sasuke will be PISSED (Imagine if Sasuke's father's eye is on the palm of his fap hand xd)
2) Sakura is going to fight and try to kill Sasuke. We know Sasuke still has a soft spot for his old team 7, even if he hides it. This is really going to stress him out.
3) Finally having to hunt Naruto down for the nine-tailed fox. This will be stressfull too.
4) I'm sure he'll have to fight Kakashi at some point too, especially if Sasuke goes after Naruto and Kakashi becomes Hokage.
5) If Karin or other Taka members get killed by Danzou or other enemies, he will be extremely upset.
All these things combine together, Sasuke could have the kind of meltdown that will lead him to gain the Rinnegan. This would enable him to control the statue to seal the additional tailed beasts.
Now that Sasuke's sharingan are almost completely powered up and he has no other good way of gaining more power (training? discipline? patience? Hell no), Madara directing him to unlock the rinnegan would be the next step for him.