I thought it was a common phrase. But Google says the contrary.
Why was Mr. Handsome talking to me? Not that I'd been hoping for that. Okay, maybe one percent of me did.
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This use of not that I'd been hoping &c is common, colloquial and grammatical.
You find that the phrase not that I'd been hoping is not common—the only instance Google finds on the entire internet is this very question.
But you're looking for the wrong thing. What's in play here is not the specific phrase not that I'd been hoping but the construction not that + finite clause. Any finite clause might occupy that final slot, and if you Google not that you'll find thousands of examples—you'd probably find hundreds of thousands if Google were willing to show you that many. And a large proportion of them are uses in an it cleft, often with the It is deleted, to deny a possible implication of what has gone before. Here are some examples—
I yelled at them for being a******s to someone on their first dungeon run, and the bard said "it's not that she's new, it's that she's not listening" —an RPG forum
Not that I care... but, why were you talking to that stupid b***h? —Urban Dictionary
Not That He Wants to Sound Chauvinistic, But Donald Trump Thinks Letting Women Work Is ‘Dangerous’ —Headline, New York Magazine
If you want to understand the 'grammar', here's how it works:
[That I'd been hoping for that] is not (true). = [ The proposition ] is not (true).
It's not [that I'd been hoping for that].
Not [that I'd been hoping for that].
† Don't be misled by the term 'conversational'. To be sure, this phenomenon is most commonly encountered in spontaneous speech; but in the particular case of not that it is also at home in formal discourse. Here it is, for instance, in a LitCrit study of a density almost impenetrable to the non-professional—
It is rare to see the originator of a critical method offer such an ironical assessment of what has been, it is true, too often systematised into simple conceptual tricks under the guise of deconstruction. Not that Derrida engages in debunking pastiche or contorted self-parody; the assessment of what passed as deconstruction nevertheless attests to the validity of the problematics—what is unbearable is that that it turns into an easy refrain, and can ‘function’ almost regardless of the text taken as example or simple precept.
—Derek Attridge, Reading and Responsibility: Deconstruction’s Traces, 2010, 152