It would be a first at YouTube, where "Baby" by Justin Bieber in February became the only other video in the billion-view club.
"Two billion views; they are very honorable and very burdensome numbers," Psy said in a statement YouTube shared with AFP on Friday.
"With the appreciation, I will come back soon with more joyful contents!"
"Gangnam Style" at the OfficialPsy channel has racked up nearly 100 million views this year, bringing it to less than 500,000 shy of the two-billion mark on midday Friday in northern California, where YouTube is based.
The video became a global sensation and fueled a South Korean "K-Pop" trend after it was uploaded to YouTube in July 2012.
Psy's follow-up song "Gentleman" set the record for the most YouTube views in a single day 38 million on April 14, 2013.
Only three percent of "Gangnam Style" views at YouTube have been from inside South Korea.
As well as propeling Psy onto the global stage, his horse-riding-style dance moves have been parodied and mimicked in myriad videos uploaded to YouTube.
The "Gangnam" in the title of the hit song is Seoul's wealthiest residential and shopping district, lined with luxury boutiques, top-end bars, nightclubs and restaurants frequented by celebrities.
Translating the song's lyrics, which some see as satirizing the area's self-importance and ostentatious wealth, offers little in the way of concrete insights.
Psy sings about being the "guy who downs boiling coffee in one shot" and who "goes completely crazy when the right time comes."
The video has Psy breezing through a world of speed boats, yoga classes and exclusive clubs all the while performing an eccentric horse-riding dance accompanied by beautiful models.