The whole point in Itachi going undercover was so that he would feed the Village with any information...
Hiruzen probably knew about the Akatsuki because Itachi told him. It was Obito who tried to recruit him after-all! Itachi knew he wasn't able to tell anyone, giving that it would but his position in danger.
He wanted Naruto to live a normal life.... The people of the village hated him enough. What do you think would happen if everyone found out that Naruto is the cause of a group of extremely dangerous ninja coming after the village?
Itachi went in to keep control on the inside. He would merely give Hiruzen an update, so that he could take the correct procedures, in-case the did try and infiltrate the village.