Worst theory yet.
We know Itachi was going blind for overuse of the Mangekyou Sharingan, this was stated by numerous people including Kakashi and Zetsu.
However, nothing about his body deteriorating was stated, and considering at the end of the fight Zetsu commented about how Itachi wasn't fighting at full, and how he started coughing up blood for no reason, it would be fair to say a completely unrelated problem caused it.
Itachi most likely knew he was going to die from that disease and left it up to Sasuke to finish off Madara.
Lastly, he didn't 'give' him the Mangekyou Sharingan, he embedded something into him, so that his Mangekyou Sharingan along with his Mangekyou Sharingan techniques would activate when seeing Madara in hopes of finishing him off. We still don't know if Sasuke can actually use the Mangekyou Sharingan.