I'm looking at the concept of Discipleship in Naruto, mainly because it seems that Sai has been overlooked.
Naruto is the Disciple of Jiraiya
Sasuke was the Disciple of Orochimaru
Sakura is the Disciple of Tsunada
Sai is the Disciple of Danzou
Kakashi is the Disciple of Minato
Minato is the Disciple of Jiraiya
Kakashi has no disciples.
I question Sai's discipleship, mainly because Danzou doesn't seem to be passing the Baton in responsibility. Also Danzou trained many under his wings and has chosen other roots to follow him to the convention.
The concept of Discipleship is important, because if you have the wrong Teacher for the student, the student would not excel.
For example, Jiraiya would have been a great teacher for Naruto, because they both are capable of handling Sage mode, both hold a lot of Chakra, and both strategically use Shadow clones. As such they are a great match.
As much as we all want Naruto to be the disciple of Kakashi, Kakashi was part of Anbu. His extremely strategic and covert training is highly inappropriate and an absolute waste of time. Hence Kakashi only trains Naruto what he trained Sasuke 3 years back.
On the one hand, Kakashi really believed Sasuke was going to be his disciple, since he was so excited that they both have the same primary Chakra type.
So we have the basic relationships established. If Kishi were to have a time skip anytime soon, the next teachers of the main characters, Sasuke, Sakura, Sai and Naruto will mould their characters further.
In my opinion, Sai is going to be the Disciple of Kakashi. Only because Kakashi is looking to being Hokage, and Yamato doesn't seem to understand Naruto quite as well as Kakashi and Sai. And hence he needs Sai to watch out for Naruto, preform sealing techniques as naruto grows.
Yamato is the disciple of the 1st Hokage, (Like he has free will...)
Sasuke would be the true disciple of Madara
Sakura would be the Disciple of Tsunada
Sai would be disciple of Kakashi.
Naruto ... is the surprise I guess.