So when we see Itachi and Shisui in the past, Shisui is the one who asks the 3rd hokage about trying to divert the Uchiha Coup on his own for which he get's approval by the third Hokage at which Danzo was also present.
When Shisui tried to use genjuitsu on his clan, he's intercepted and attacked by Danzo, surely the hokage didn't approve of that. Shisui was able to tell Itachi of what happened, but why didn't Itachi tell the Hokage about Danzo's betrayal?