So, I'm pretty sure that's not entirely accurate. What Claudia says is "like an older sister" (chotto onee-san, I think). I think it's the same in the jp version of the original? can't really confirm that though.
I don't want to be that guy, but from what I've heard, obviously cannot confirm this because I'm not Japanese, older sisters are seen as responsible, that's what Claudia is referring to, someone who's responsible and can take care of him, the english just hyperfocuses on the "older" part, but the person's age isn't really what's relevant here.
I can't subscribe to Aerith being the one hinted at here by Claudia, especially not after, just a few days before this scene chronologically, Tifa told Claudia ambitions Cloud has that he didn't tell his mother. From her reaction, I think it's obvious she came to a conclusion in her head about Cloud and his motivations.