Board Thread:Naruto Discussions/@comment-7292165-20140715160041/@comment-1251315-20140716114111

Seelentau wrote: Itachi said that the Kyubi was their target (his and Kisame's). Since Kisame got the Yonbi, Itachi must've been assigned to Kyubi. There's not actual proof that they specifically stated "Naruto's my target": pre timeskip, they just said "our target" in reference to the Akatsuki, not themselves, since Kishimoto hadn't come up with any background for the other Akatsuki members at that point.

Plus, it was just a cover story if they got caught in the village, since Itachi only went to Konoha to check on Sasuke and he couldn't just come out and say that he was there to check on his brother. Post timeskip, Itachi was tasked to capture Naruto only because it was the most appropriate for him to do it, but don't forget that it was a clone in that instance.

At no point in the series has anyone been definitely tasked with getting Naruto, excepting Pain when Obito (disguised as "Madara") asked Pain to go and get him.