I thought of a possible way for the rasengan to defend it's user similar to how Sasake covers himself with Amaterasu (blaze release). Lol I know we are all sick of the rasengan variations but you might see this one as a refreshing change. Before i get into this any further I just wanted to say how the rasengn does damage and how it can protect naruto. The way the resengan does it's damage is when you ram it into something, so I thought what about the opposite. What if something else was raming into rasengan. The rasengan in theory would resist the whats coming at it. Essentially the same thing is happening but from a different perceptive.
It will only be possible in sage mode/chakra cloak modes and that goes for all shinobi with the exception of Byakugan users ( I'll elaborate about them later).
Now in true sage mode, I think you all remember when in true sage mode the user is encased in senjutsu chakra like an aura which makes the taijutsu style Frog fu hard to deal with. Basically my idea is since there's sage chakra all around the user he/she could in theory through shape manipulation form a rasengan all around there body the same why they do in the palms. So it would will look like someone inside a rasengan, which could protect Naruto against Amaterasu and maybe Susanoo.
Here's a page showing Naruto covered in sage chakra.
I also think the same thing could be done by Byakugan users as they can release chakra from all their tenketsu at once and surround themselves in chakra. There is already the Eight Trigrams Palms Heavenly Spin technique but I guess in this case the user doesn't have to spin physically.
Here's a page showing Neji's ability to release chakra from all his tenketsu.
This does sound out there but you gotta say after we saw Sasake surround himself in Amaterasu anything is possible. What you guys think?
The recent chapter(515) shows a cool picture naruto using his cloak to form rasengans. The thing that caught my eye was the fact he didn't need his hands to make the rasengans or it looked like that anyway. It technically wasn't part of the plot section of the manga but interesting none the less.
Back to the point for naruto or anyone for that matter to make rasengan around his body he would need to be able to make a rasengan without his hands which could be implied in this picture.
Not exactly evidence but worth a thought.