Pomeranian Lover
I'm not sure of an exact origin, but it might come from a general trend where a major character falls in love with an upperclassman. From what I've seen in anime, the larger trope is that of a super popular and admired student (can be male or female) who is usually at least a 2nd or 3rd year in their school. Which then leads to this admiration turning into an infatuation or romantic crush on the older student.
One specific example of "senpai" being associated with romance is from Sailor Moon, where Makoto Kino had an unrequited crush on an upperclassman at her former school, which leads her to be attracted to boys who resemble her old "senpai" in some way. There's even one episode in SuperS where Usagi and her friends suspect that Chibi-Usa has someone she's in love with, and Makoto assumes that whoever it is must be Chibi-Usa's senpai from school because "that's how it usually is" according to her.
Edit: I found a page that explains where the specific "I hope senpai will notice me" meme comes from, if that helps.
https://knowyourmeme.com/memes/i-hope-senpai-will-notice-me
Edited by Rainbow on Feb 24th 2019 at 2:43:09 PM
I've noticed that "senpai" as a fanspeak term and 'senpai' as an honorific have very different meanings. While the honorific means an immediate superior (or upperclassman, or something like that), as a fanspeak term, it pretty much means a crush, like the "waiting for senpai to notice me" relationship status.
What I'm wondering is, where did this meaning as a fanspeak term come from? Obviously it's from a harem anime, but where?