Forgive my frankness but it seems to me you both not only misunderstand the character but also his motivation as an indirect and shrewd guardian.
The loving brother stuff is plain garbage! He had pushed his deception to sasuke up to well after he was sick and up to the very point of his death. Where in the entire battle between sasuke and itachi would be an appropriate moment for itachi to say what you think he would have? Edo itachi? Oh please, he was almost indifferent to sasuke even knowing of izanagi. Not only that, itachi never opened the style of dialogue that would have served a working context to talk about rinnegan. He was a loving brother but you are completely ignoring the complexity of how that relationship worked. It was full of deceits and shame and never a direct warning for sasukes well being.
The loving brother did not exist to sasuke after the massacre until tobi told the truth. You also forget that itachi's manipulations pushed sasuke the young boy into the fold of orochimaru and later akatsuki! Itachi planned and manipulated sasuke into the company of the very same people you think Mr loving brother is going to warn sasuke about being used by. I'd say more but that's for another thread and its the main reason i enjoy kishimoto.
Warning sasuke about rinnegan or mentioning it was making him sick destroys what he wanted to accomplish through his manipulation of sasuke (it extends further than just him and sasuke), defies his character, and sabotages all other motives.
The issue of sasuke or not getting rinnegan needs separate discussion but it does tie into this particular argument IM making here and further establishes why itachi would most certainly keep his mouth shut.
Back on topic, itachi's illness is well within the realm of possibility being an onsetting mutation/evolution of his sharingan into rinnegan. Going off topic, it would harm him on several levels beyond just his physical condition. It would have adverse effects on his goals and would severely imbalance power within akatsuki. If it is revealed he did indeed near rinnegan then it will be revealed he willingly tried to suppress it. It would be up to sasuke to harness that power at the APPROPRIATE TIME!!