I'm gonna say that Kushina was lying to Mikoto. After all, when Minato died Itachi hadn't yet entered the academy, let alone made a name for himself.
Author's response
I'm going to have to disagree with you there. By the time Minato had died Itachi was definitely in the academy as he graduated at age 7. Which he then graduated at the top of his class. To me a Hokage is constantly looking out for the next person they plan to elavate. I think even at a very young age Itachi would be on a very short list of people Minato would consider and keep an eye on.