The reviewer at AV Club has this Insane, Obviously Wrong Theory:
Look, any garden-variety Doctor Who crackpot theorist can suggest that Clara is the Rani, because every female character we’ve seen on Doctor Who since 1985 is probably the Rani. But I’ll do you one better—what if the reason the TARDIS doesn’t trust Clara is because Clara is actually a TARDIS herself? The Rani is a scientist, after all, so perhaps she devised a chameleon circuit that takes on the form of living beings… except, much like the Doctor’s TARDIS, it got stuck on one appearance, which is why an identical-looking young woman keeps popping up in different time periods, and her apparent deaths are just dematerializations. So then, Clara is the Rani’s TARDIS. Also, she’s also the Rani, because, well… why not?
It's a crazy theory and it's probably not true...and yet, it makes some sense.
I would love it if she was a TARDIS. (Of course, there would be endless fanboy jokes about getting inside, the inside being bigger, blah blah blah)
But, a humanoid as Tardis would be so weird on TV (didn't they do that on the radio stories?) that it would be fantastic.
But, it's not going to happen.
Like we will never see the Rani again.