He is not awakening the rinnegan and will never be.
It took 100 years for madara to awaken the rinnegan.Sasuke awakening the rinnegan in short periods of time wont make any sense and it will destroy logic.
Logic hasn't existed in the Narutoverse for a long time now sadly.
No Rinnegan for Sasuke its stupid, Naruto is destined to be the strongest ninja in the end and he has been more than hinted to get the Rinnegan! If you remember seeing the shadow of the Rinnegan used with the Bijuus chakra he gotten except the 1 and 8 tailed that spooked Juubi.
The shadow of the face with the Rinnegan was not meant to mean that Naruto will get the Rinnegan, it was meant to show that the Juubi sees the Sage of Six Paths in Naruto, and got angry/scared/whatever because of that. Naruto had just saved everyone and himself from the Juubi's big ass, land changing attack. The Juubi basically had a "flashback" of sorts, reminding him of the only other person who was powerful enough to stand against him, which was the Sage of the Six Paths. If anything that image was foreshadowing Naruto becoming the Sage, not him getting the Rinnegan.
Pay attention to the manga; The only reason it took Madara so long is because he use degraded Senju DNA in the form of Zetsu material. Kabuto has the proper Hashirama DNA from Orochimaru's proper cloning technique so Sasuke's results will be near immediate and maybe even stronger.
Uhhh, why don't you pay attention to the manga? When did Madara ever say he implanted Zetsu's degraded Hashi DNA into himself? He implanted Hashi's pure DNA he took from Hashi himself after the battle at the valley of the end. He didn't even make any Zetsu's until AFTER he awakened the Rinnegan, because he used the Gedo statue to make the Zetsu, and he didn't get the Gedo statue until after he awakened the Rinnegan obviously. The Zetsu's are cloned from the Gedo statue, that's why they are degraded material or whatever, not the Hashi DNA in Madara himself though.
Can we really say logic exists anymore in the Narutoverse?
Nope. Been gone for a while.